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Add the qra64 files.

This commit is contained in:
Joe Taylor 2018-10-19 15:55:29 -04:00
parent 11cc9ab579
commit 436daf17b0
27 changed files with 7511 additions and 0 deletions
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30
libm65/qra64/Makefile.Win Normal file
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FC = gfortran
CC = gcc
CFLAGS = -O2 -Wall -I. -D_WIN32
# Default rules
%.o: %.c
${CC} ${CFLAGS} -c $<
%.o: %.f
${FC} ${FFLAGS} -c $<
%.o: %.F
${FC} ${FFLAGS} -c $<
%.o: %.f90
${FC} ${FFLAGS} -c $<
%.o: %.F90
${FC} ${FFLAGS} -c $<
all: qra64.exe
OBJS1 = main.o qra64.o
qra64.exe: $(OBJS1)
${CC} -o qra64.exe $(OBJS1) ../qracodes/libqra64.a -lm
OBJS2 = qra64sim.o options.o wavhdr.o
qra64sim.exe: $(OBJS2)
${FC} -o qra64sim.exe $(OBJS2) ../qracodes/libqra64.a -lm
.PHONY : clean
clean:
$(RM) *.o qra64.exe qra64sim.exe

302
libm65/qra64/fadengauss.c Normal file
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// Gaussian energy fading tables for QRA64
static const int glen_tab_gauss[64] = {
2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2,
3, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 5, 5, 5, 6,
6, 6, 7, 7, 8, 8, 9, 10,
10, 11, 12, 13, 14, 15, 17, 18,
19, 21, 23, 25, 27, 29, 32, 34,
37, 41, 44, 48, 52, 57, 62, 65
};
static const float ggauss1[2] = {
0.0296f, 0.9101f
};
static const float ggauss2[2] = {
0.0350f, 0.8954f
};
static const float ggauss3[2] = {
0.0411f, 0.8787f
};
static const float ggauss4[2] = {
0.0483f, 0.8598f
};
static const float ggauss5[2] = {
0.0566f, 0.8387f
};
static const float ggauss6[2] = {
0.0660f, 0.8154f
};
static const float ggauss7[2] = {
0.0767f, 0.7898f
};
static const float ggauss8[2] = {
0.0886f, 0.7621f
};
static const float ggauss9[2] = {
0.1017f, 0.7325f
};
static const float ggauss10[2] = {
0.1159f, 0.7012f
};
static const float ggauss11[2] = {
0.1310f, 0.6687f
};
static const float ggauss12[2] = {
0.1465f, 0.6352f
};
static const float ggauss13[2] = {
0.1621f, 0.6013f
};
static const float ggauss14[2] = {
0.1771f, 0.5674f
};
static const float ggauss15[2] = {
0.1911f, 0.5339f
};
static const float ggauss16[2] = {
0.2034f, 0.5010f
};
static const float ggauss17[3] = {
0.0299f, 0.2135f, 0.4690f
};
static const float ggauss18[3] = {
0.0369f, 0.2212f, 0.4383f
};
static const float ggauss19[3] = {
0.0454f, 0.2263f, 0.4088f
};
static const float ggauss20[3] = {
0.0552f, 0.2286f, 0.3806f
};
static const float ggauss21[3] = {
0.0658f, 0.2284f, 0.3539f
};
static const float ggauss22[3] = {
0.0766f, 0.2258f, 0.3287f
};
static const float ggauss23[3] = {
0.0869f, 0.2212f, 0.3049f
};
static const float ggauss24[3] = {
0.0962f, 0.2148f, 0.2826f
};
static const float ggauss25[4] = {
0.0351f, 0.1041f, 0.2071f, 0.2616f
};
static const float ggauss26[4] = {
0.0429f, 0.1102f, 0.1984f, 0.2420f
};
static const float ggauss27[4] = {
0.0508f, 0.1145f, 0.1890f, 0.2237f
};
static const float ggauss28[4] = {
0.0582f, 0.1169f, 0.1791f, 0.2067f
};
static const float ggauss29[5] = {
0.0289f, 0.0648f, 0.1176f, 0.1689f, 0.1908f
};
static const float ggauss30[5] = {
0.0351f, 0.0703f, 0.1168f, 0.1588f, 0.1760f
};
static const float ggauss31[5] = {
0.0411f, 0.0745f, 0.1146f, 0.1488f, 0.1623f
};
static const float ggauss32[6] = {
0.0246f, 0.0466f, 0.0773f, 0.1115f, 0.1390f, 0.1497f
};
static const float ggauss33[6] = {
0.0297f, 0.0512f, 0.0788f, 0.1075f, 0.1295f, 0.1379f
};
static const float ggauss34[6] = {
0.0345f, 0.0549f, 0.0791f, 0.1029f, 0.1205f, 0.1270f
};
static const float ggauss35[7] = {
0.0240f, 0.0387f, 0.0575f, 0.0784f, 0.0979f, 0.1118f, 0.1169f
};
static const float ggauss36[7] = {
0.0281f, 0.0422f, 0.0590f, 0.0767f, 0.0926f, 0.1037f, 0.1076f
};
static const float ggauss37[8] = {
0.0212f, 0.0318f, 0.0449f, 0.0596f, 0.0744f, 0.0872f, 0.0960f, 0.0991f
};
static const float ggauss38[8] = {
0.0247f, 0.0348f, 0.0467f, 0.0593f, 0.0716f, 0.0819f, 0.0887f, 0.0911f
};
static const float ggauss39[9] = {
0.0199f, 0.0278f, 0.0372f, 0.0476f, 0.0584f, 0.0684f, 0.0766f, 0.0819f,
0.0838f
};
static const float ggauss40[10] = {
0.0166f, 0.0228f, 0.0303f, 0.0388f, 0.0478f, 0.0568f, 0.0649f, 0.0714f,
0.0756f, 0.0771f
};
static const float ggauss41[10] = {
0.0193f, 0.0254f, 0.0322f, 0.0397f, 0.0474f, 0.0548f, 0.0613f, 0.0664f,
0.0697f, 0.0709f
};
static const float ggauss42[11] = {
0.0168f, 0.0217f, 0.0273f, 0.0335f, 0.0399f, 0.0464f, 0.0524f, 0.0576f,
0.0617f, 0.0643f, 0.0651f
};
static const float ggauss43[12] = {
0.0151f, 0.0191f, 0.0237f, 0.0288f, 0.0342f, 0.0396f, 0.0449f, 0.0498f,
0.0540f, 0.0572f, 0.0592f, 0.0599f
};
static const float ggauss44[13] = {
0.0138f, 0.0171f, 0.0210f, 0.0252f, 0.0297f, 0.0343f, 0.0388f, 0.0432f,
0.0471f, 0.0504f, 0.0529f, 0.0545f, 0.0550f
};
static const float ggauss45[14] = {
0.0128f, 0.0157f, 0.0189f, 0.0224f, 0.0261f, 0.0300f, 0.0339f, 0.0377f,
0.0412f, 0.0444f, 0.0470f, 0.0489f, 0.0501f, 0.0505f
};
static const float ggauss46[15] = {
0.0121f, 0.0146f, 0.0173f, 0.0202f, 0.0234f, 0.0266f, 0.0299f, 0.0332f,
0.0363f, 0.0391f, 0.0416f, 0.0437f, 0.0452f, 0.0461f, 0.0464f
};
static const float ggauss47[17] = {
0.0097f, 0.0116f, 0.0138f, 0.0161f, 0.0186f, 0.0212f, 0.0239f, 0.0267f,
0.0294f, 0.0321f, 0.0346f, 0.0369f, 0.0389f, 0.0405f, 0.0417f, 0.0424f,
0.0427f
};
static const float ggauss48[18] = {
0.0096f, 0.0113f, 0.0131f, 0.0151f, 0.0172f, 0.0194f, 0.0217f, 0.0241f,
0.0264f, 0.0287f, 0.0308f, 0.0329f, 0.0347f, 0.0362f, 0.0375f, 0.0384f,
0.0390f, 0.0392f
};
static const float ggauss49[19] = {
0.0095f, 0.0110f, 0.0126f, 0.0143f, 0.0161f, 0.0180f, 0.0199f, 0.0219f,
0.0239f, 0.0258f, 0.0277f, 0.0294f, 0.0310f, 0.0325f, 0.0337f, 0.0347f,
0.0354f, 0.0358f, 0.0360f
};
static const float ggauss50[21] = {
0.0083f, 0.0095f, 0.0108f, 0.0122f, 0.0136f, 0.0152f, 0.0168f, 0.0184f,
0.0201f, 0.0217f, 0.0234f, 0.0250f, 0.0265f, 0.0279f, 0.0292f, 0.0303f,
0.0313f, 0.0320f, 0.0326f, 0.0329f, 0.0330f
};
static const float ggauss51[23] = {
0.0074f, 0.0084f, 0.0095f, 0.0106f, 0.0118f, 0.0131f, 0.0144f, 0.0157f,
0.0171f, 0.0185f, 0.0199f, 0.0213f, 0.0227f, 0.0240f, 0.0252f, 0.0263f,
0.0273f, 0.0282f, 0.0290f, 0.0296f, 0.0300f, 0.0303f, 0.0303f
};
static const float ggauss52[25] = {
0.0068f, 0.0076f, 0.0085f, 0.0094f, 0.0104f, 0.0115f, 0.0126f, 0.0137f,
0.0149f, 0.0160f, 0.0172f, 0.0184f, 0.0196f, 0.0207f, 0.0218f, 0.0228f,
0.0238f, 0.0247f, 0.0255f, 0.0262f, 0.0268f, 0.0273f, 0.0276f, 0.0278f,
0.0279f
};
static const float ggauss53[27] = {
0.0063f, 0.0070f, 0.0078f, 0.0086f, 0.0094f, 0.0103f, 0.0112f, 0.0121f,
0.0131f, 0.0141f, 0.0151f, 0.0161f, 0.0170f, 0.0180f, 0.0190f, 0.0199f,
0.0208f, 0.0216f, 0.0224f, 0.0231f, 0.0237f, 0.0243f, 0.0247f, 0.0251f,
0.0254f, 0.0255f, 0.0256f
};
static const float ggauss54[29] = {
0.0060f, 0.0066f, 0.0072f, 0.0079f, 0.0086f, 0.0093f, 0.0101f, 0.0109f,
0.0117f, 0.0125f, 0.0133f, 0.0142f, 0.0150f, 0.0159f, 0.0167f, 0.0175f,
0.0183f, 0.0190f, 0.0197f, 0.0204f, 0.0210f, 0.0216f, 0.0221f, 0.0225f,
0.0228f, 0.0231f, 0.0233f, 0.0234f, 0.0235f
};
static const float ggauss55[32] = {
0.0053f, 0.0058f, 0.0063f, 0.0068f, 0.0074f, 0.0080f, 0.0086f, 0.0093f,
0.0099f, 0.0106f, 0.0113f, 0.0120f, 0.0127f, 0.0134f, 0.0141f, 0.0148f,
0.0155f, 0.0162f, 0.0168f, 0.0174f, 0.0180f, 0.0186f, 0.0191f, 0.0196f,
0.0201f, 0.0204f, 0.0208f, 0.0211f, 0.0213f, 0.0214f, 0.0215f, 0.0216f
};
static const float ggauss56[34] = {
0.0052f, 0.0056f, 0.0060f, 0.0065f, 0.0070f, 0.0075f, 0.0080f, 0.0086f,
0.0091f, 0.0097f, 0.0103f, 0.0109f, 0.0115f, 0.0121f, 0.0127f, 0.0133f,
0.0138f, 0.0144f, 0.0150f, 0.0155f, 0.0161f, 0.0166f, 0.0170f, 0.0175f,
0.0179f, 0.0183f, 0.0186f, 0.0189f, 0.0192f, 0.0194f, 0.0196f, 0.0197f,
0.0198f, 0.0198f
};
static const float ggauss57[37] = {
0.0047f, 0.0051f, 0.0055f, 0.0058f, 0.0063f, 0.0067f, 0.0071f, 0.0076f,
0.0080f, 0.0085f, 0.0090f, 0.0095f, 0.0100f, 0.0105f, 0.0110f, 0.0115f,
0.0120f, 0.0125f, 0.0130f, 0.0134f, 0.0139f, 0.0144f, 0.0148f, 0.0152f,
0.0156f, 0.0160f, 0.0164f, 0.0167f, 0.0170f, 0.0173f, 0.0175f, 0.0177f,
0.0179f, 0.0180f, 0.0181f, 0.0181f, 0.0182f
};
static const float ggauss58[41] = {
0.0041f, 0.0044f, 0.0047f, 0.0050f, 0.0054f, 0.0057f, 0.0060f, 0.0064f,
0.0068f, 0.0072f, 0.0076f, 0.0080f, 0.0084f, 0.0088f, 0.0092f, 0.0096f,
0.0101f, 0.0105f, 0.0109f, 0.0113f, 0.0117f, 0.0121f, 0.0125f, 0.0129f,
0.0133f, 0.0137f, 0.0140f, 0.0144f, 0.0147f, 0.0150f, 0.0153f, 0.0155f,
0.0158f, 0.0160f, 0.0162f, 0.0163f, 0.0164f, 0.0165f, 0.0166f, 0.0167f,
0.0167f
};
static const float ggauss59[44] = {
0.0039f, 0.0042f, 0.0044f, 0.0047f, 0.0050f, 0.0053f, 0.0056f, 0.0059f,
0.0062f, 0.0065f, 0.0068f, 0.0072f, 0.0075f, 0.0079f, 0.0082f, 0.0086f,
0.0089f, 0.0093f, 0.0096f, 0.0100f, 0.0104f, 0.0107f, 0.0110f, 0.0114f,
0.0117f, 0.0120f, 0.0124f, 0.0127f, 0.0130f, 0.0132f, 0.0135f, 0.0138f,
0.0140f, 0.0142f, 0.0144f, 0.0146f, 0.0148f, 0.0149f, 0.0150f, 0.0151f,
0.0152f, 0.0153f, 0.0153f, 0.0153f
};
static const float ggauss60[48] = {
0.0036f, 0.0038f, 0.0040f, 0.0042f, 0.0044f, 0.0047f, 0.0049f, 0.0052f,
0.0055f, 0.0057f, 0.0060f, 0.0063f, 0.0066f, 0.0068f, 0.0071f, 0.0074f,
0.0077f, 0.0080f, 0.0083f, 0.0086f, 0.0089f, 0.0092f, 0.0095f, 0.0098f,
0.0101f, 0.0104f, 0.0107f, 0.0109f, 0.0112f, 0.0115f, 0.0117f, 0.0120f,
0.0122f, 0.0124f, 0.0126f, 0.0128f, 0.0130f, 0.0132f, 0.0134f, 0.0135f,
0.0136f, 0.0137f, 0.0138f, 0.0139f, 0.0140f, 0.0140f, 0.0140f, 0.0140f
};
static const float ggauss61[52] = {
0.0033f, 0.0035f, 0.0037f, 0.0039f, 0.0041f, 0.0043f, 0.0045f, 0.0047f,
0.0049f, 0.0051f, 0.0053f, 0.0056f, 0.0058f, 0.0060f, 0.0063f, 0.0065f,
0.0068f, 0.0070f, 0.0073f, 0.0075f, 0.0078f, 0.0080f, 0.0083f, 0.0085f,
0.0088f, 0.0090f, 0.0093f, 0.0095f, 0.0098f, 0.0100f, 0.0102f, 0.0105f,
0.0107f, 0.0109f, 0.0111f, 0.0113f, 0.0115f, 0.0116f, 0.0118f, 0.0120f,
0.0121f, 0.0122f, 0.0124f, 0.0125f, 0.0126f, 0.0126f, 0.0127f, 0.0128f,
0.0128f, 0.0129f, 0.0129f, 0.0129f
};
static const float ggauss62[57] = {
0.0030f, 0.0031f, 0.0033f, 0.0034f, 0.0036f, 0.0038f, 0.0039f, 0.0041f,
0.0043f, 0.0045f, 0.0047f, 0.0048f, 0.0050f, 0.0052f, 0.0054f, 0.0056f,
0.0058f, 0.0060f, 0.0063f, 0.0065f, 0.0067f, 0.0069f, 0.0071f, 0.0073f,
0.0075f, 0.0077f, 0.0080f, 0.0082f, 0.0084f, 0.0086f, 0.0088f, 0.0090f,
0.0092f, 0.0094f, 0.0096f, 0.0097f, 0.0099f, 0.0101f, 0.0103f, 0.0104f,
0.0106f, 0.0107f, 0.0108f, 0.0110f, 0.0111f, 0.0112f, 0.0113f, 0.0114f,
0.0115f, 0.0116f, 0.0116f, 0.0117f, 0.0117f, 0.0118f, 0.0118f, 0.0118f,
0.0118f
};
static const float ggauss63[62] = {
0.0027f, 0.0029f, 0.0030f, 0.0031f, 0.0032f, 0.0034f, 0.0035f, 0.0037f,
0.0038f, 0.0040f, 0.0041f, 0.0043f, 0.0045f, 0.0046f, 0.0048f, 0.0049f,
0.0051f, 0.0053f, 0.0055f, 0.0056f, 0.0058f, 0.0060f, 0.0062f, 0.0063f,
0.0065f, 0.0067f, 0.0069f, 0.0071f, 0.0072f, 0.0074f, 0.0076f, 0.0078f,
0.0079f, 0.0081f, 0.0083f, 0.0084f, 0.0086f, 0.0088f, 0.0089f, 0.0091f,
0.0092f, 0.0094f, 0.0095f, 0.0096f, 0.0098f, 0.0099f, 0.0100f, 0.0101f,
0.0102f, 0.0103f, 0.0104f, 0.0105f, 0.0105f, 0.0106f, 0.0107f, 0.0107f,
0.0108f, 0.0108f, 0.0108f, 0.0108f, 0.0109f, 0.0109f
};
static const float ggauss64[65] = {
0.0028f, 0.0029f, 0.0030f, 0.0031f, 0.0032f, 0.0034f, 0.0035f, 0.0036f,
0.0037f, 0.0039f, 0.0040f, 0.0041f, 0.0043f, 0.0044f, 0.0046f, 0.0047f,
0.0048f, 0.0050f, 0.0051f, 0.0053f, 0.0054f, 0.0056f, 0.0057f, 0.0059f,
0.0060f, 0.0062f, 0.0063f, 0.0065f, 0.0066f, 0.0068f, 0.0069f, 0.0071f,
0.0072f, 0.0074f, 0.0075f, 0.0077f, 0.0078f, 0.0079f, 0.0081f, 0.0082f,
0.0083f, 0.0084f, 0.0086f, 0.0087f, 0.0088f, 0.0089f, 0.0090f, 0.0091f,
0.0092f, 0.0093f, 0.0094f, 0.0094f, 0.0095f, 0.0096f, 0.0097f, 0.0097f,
0.0098f, 0.0098f, 0.0099f, 0.0099f, 0.0099f, 0.0099f, 0.0100f, 0.0100f,
0.0100f
};
static const float *gptr_tab_gauss[64] = {
ggauss1, ggauss2, ggauss3, ggauss4,
ggauss5, ggauss6, ggauss7, ggauss8,
ggauss9, ggauss10, ggauss11, ggauss12,
ggauss13, ggauss14, ggauss15, ggauss16,
ggauss17, ggauss18, ggauss19, ggauss20,
ggauss21, ggauss22, ggauss23, ggauss24,
ggauss25, ggauss26, ggauss27, ggauss28,
ggauss29, ggauss30, ggauss31, ggauss32,
ggauss33, ggauss34, ggauss35, ggauss36,
ggauss37, ggauss38, ggauss39, ggauss40,
ggauss41, ggauss42, ggauss43, ggauss44,
ggauss45, ggauss46, ggauss47, ggauss48,
ggauss49, ggauss50, ggauss51, ggauss52,
ggauss53, ggauss54, ggauss55, ggauss56,
ggauss57, ggauss58, ggauss59, ggauss60,
ggauss61, ggauss62, ggauss63, ggauss64
};

304
libm65/qra64/fadenlorentz.c Normal file
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// Lorentz energy fading tables for QRA64
static const int glen_tab_lorentz[64] = {
2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 3, 3,
3, 3, 3, 3, 3, 4, 4, 4,
4, 4, 5, 5, 5, 5, 6, 6,
7, 7, 7, 8, 8, 9, 10, 10,
11, 12, 13, 14, 15, 16, 17, 19,
20, 22, 23, 25, 27, 30, 32, 35,
38, 41, 45, 49, 53, 57, 62, 65
};
static const float glorentz1[2] = {
0.0214f, 0.9107f
};
static const float glorentz2[2] = {
0.0244f, 0.9030f
};
static const float glorentz3[2] = {
0.0280f, 0.8950f
};
static const float glorentz4[2] = {
0.0314f, 0.8865f
};
static const float glorentz5[2] = {
0.0349f, 0.8773f
};
static const float glorentz6[2] = {
0.0388f, 0.8675f
};
static const float glorentz7[2] = {
0.0426f, 0.8571f
};
static const float glorentz8[2] = {
0.0463f, 0.8459f
};
static const float glorentz9[2] = {
0.0500f, 0.8339f
};
static const float glorentz10[2] = {
0.0538f, 0.8210f
};
static const float glorentz11[2] = {
0.0579f, 0.8074f
};
static const float glorentz12[2] = {
0.0622f, 0.7930f
};
static const float glorentz13[2] = {
0.0668f, 0.7777f
};
static const float glorentz14[2] = {
0.0715f, 0.7616f
};
static const float glorentz15[3] = {
0.0196f, 0.0765f, 0.7445f
};
static const float glorentz16[3] = {
0.0210f, 0.0816f, 0.7267f
};
static const float glorentz17[3] = {
0.0226f, 0.0870f, 0.7080f
};
static const float glorentz18[3] = {
0.0242f, 0.0925f, 0.6885f
};
static const float glorentz19[3] = {
0.0259f, 0.0981f, 0.6682f
};
static const float glorentz20[3] = {
0.0277f, 0.1039f, 0.6472f
};
static const float glorentz21[3] = {
0.0296f, 0.1097f, 0.6255f
};
static const float glorentz22[4] = {
0.0143f, 0.0316f, 0.1155f, 0.6031f
};
static const float glorentz23[4] = {
0.0153f, 0.0337f, 0.1213f, 0.5803f
};
static const float glorentz24[4] = {
0.0163f, 0.0358f, 0.1270f, 0.5570f
};
static const float glorentz25[4] = {
0.0174f, 0.0381f, 0.1325f, 0.5333f
};
static const float glorentz26[4] = {
0.0186f, 0.0405f, 0.1378f, 0.5095f
};
static const float glorentz27[5] = {
0.0113f, 0.0198f, 0.0429f, 0.1428f, 0.4855f
};
static const float glorentz28[5] = {
0.0120f, 0.0211f, 0.0455f, 0.1473f, 0.4615f
};
static const float glorentz29[5] = {
0.0129f, 0.0225f, 0.0481f, 0.1514f, 0.4376f
};
static const float glorentz30[5] = {
0.0137f, 0.0239f, 0.0508f, 0.1549f, 0.4140f
};
static const float glorentz31[6] = {
0.0095f, 0.0147f, 0.0254f, 0.0536f, 0.1578f, 0.3907f
};
static const float glorentz32[6] = {
0.0101f, 0.0156f, 0.0270f, 0.0564f, 0.1600f, 0.3680f
};
static const float glorentz33[7] = {
0.0076f, 0.0109f, 0.0167f, 0.0287f, 0.0592f, 0.1614f, 0.3458f
};
static const float glorentz34[7] = {
0.0081f, 0.0116f, 0.0178f, 0.0305f, 0.0621f, 0.1620f, 0.3243f
};
static const float glorentz35[7] = {
0.0087f, 0.0124f, 0.0190f, 0.0324f, 0.0649f, 0.1618f, 0.3035f
};
static const float glorentz36[8] = {
0.0069f, 0.0093f, 0.0133f, 0.0203f, 0.0343f, 0.0676f, 0.1607f, 0.2836f
};
static const float glorentz37[8] = {
0.0074f, 0.0100f, 0.0142f, 0.0216f, 0.0362f, 0.0702f, 0.1588f, 0.2645f
};
static const float glorentz38[9] = {
0.0061f, 0.0080f, 0.0107f, 0.0152f, 0.0230f, 0.0382f, 0.0726f, 0.1561f,
0.2464f
};
static const float glorentz39[10] = {
0.0052f, 0.0066f, 0.0086f, 0.0115f, 0.0162f, 0.0244f, 0.0402f, 0.0747f,
0.1526f, 0.2291f
};
static const float glorentz40[10] = {
0.0056f, 0.0071f, 0.0092f, 0.0123f, 0.0173f, 0.0259f, 0.0422f, 0.0766f,
0.1484f, 0.2128f
};
static const float glorentz41[11] = {
0.0049f, 0.0061f, 0.0076f, 0.0098f, 0.0132f, 0.0184f, 0.0274f, 0.0441f,
0.0780f, 0.1437f, 0.1975f
};
static const float glorentz42[12] = {
0.0044f, 0.0053f, 0.0065f, 0.0082f, 0.0106f, 0.0141f, 0.0196f, 0.0290f,
0.0460f, 0.0791f, 0.1384f, 0.1831f
};
static const float glorentz43[13] = {
0.0040f, 0.0048f, 0.0057f, 0.0070f, 0.0088f, 0.0113f, 0.0150f, 0.0209f,
0.0305f, 0.0477f, 0.0797f, 0.1327f, 0.1695f
};
static const float glorentz44[14] = {
0.0037f, 0.0043f, 0.0051f, 0.0062f, 0.0075f, 0.0094f, 0.0121f, 0.0160f,
0.0221f, 0.0321f, 0.0493f, 0.0799f, 0.1267f, 0.1568f
};
static const float glorentz45[15] = {
0.0035f, 0.0040f, 0.0047f, 0.0055f, 0.0066f, 0.0081f, 0.0101f, 0.0129f,
0.0171f, 0.0234f, 0.0335f, 0.0506f, 0.0795f, 0.1204f, 0.1450f
};
static const float glorentz46[16] = {
0.0033f, 0.0037f, 0.0043f, 0.0050f, 0.0059f, 0.0071f, 0.0087f, 0.0108f,
0.0138f, 0.0181f, 0.0246f, 0.0349f, 0.0517f, 0.0786f, 0.1141f, 0.1340f
};
static const float glorentz47[17] = {
0.0031f, 0.0035f, 0.0040f, 0.0046f, 0.0054f, 0.0064f, 0.0077f, 0.0093f,
0.0116f, 0.0147f, 0.0192f, 0.0259f, 0.0362f, 0.0525f, 0.0773f, 0.1076f,
0.1237f
};
static const float glorentz48[19] = {
0.0027f, 0.0030f, 0.0034f, 0.0038f, 0.0043f, 0.0050f, 0.0058f, 0.0069f,
0.0082f, 0.0100f, 0.0123f, 0.0156f, 0.0203f, 0.0271f, 0.0374f, 0.0530f,
0.0755f, 0.1013f, 0.1141f
};
static const float glorentz49[20] = {
0.0026f, 0.0029f, 0.0032f, 0.0036f, 0.0041f, 0.0047f, 0.0054f, 0.0063f,
0.0074f, 0.0088f, 0.0107f, 0.0131f, 0.0165f, 0.0213f, 0.0282f, 0.0383f,
0.0531f, 0.0734f, 0.0950f, 0.1053f
};
static const float glorentz50[22] = {
0.0023f, 0.0025f, 0.0028f, 0.0031f, 0.0035f, 0.0039f, 0.0044f, 0.0050f,
0.0058f, 0.0067f, 0.0079f, 0.0094f, 0.0114f, 0.0139f, 0.0175f, 0.0223f,
0.0292f, 0.0391f, 0.0529f, 0.0709f, 0.0889f, 0.0971f
};
static const float glorentz51[23] = {
0.0023f, 0.0025f, 0.0027f, 0.0030f, 0.0034f, 0.0037f, 0.0042f, 0.0048f,
0.0054f, 0.0062f, 0.0072f, 0.0085f, 0.0100f, 0.0121f, 0.0148f, 0.0184f,
0.0233f, 0.0301f, 0.0396f, 0.0524f, 0.0681f, 0.0829f, 0.0894f
};
static const float glorentz52[25] = {
0.0021f, 0.0023f, 0.0025f, 0.0027f, 0.0030f, 0.0033f, 0.0036f, 0.0040f,
0.0045f, 0.0051f, 0.0058f, 0.0067f, 0.0077f, 0.0090f, 0.0107f, 0.0128f,
0.0156f, 0.0192f, 0.0242f, 0.0308f, 0.0398f, 0.0515f, 0.0650f, 0.0772f,
0.0824f
};
static const float glorentz53[27] = {
0.0019f, 0.0021f, 0.0022f, 0.0024f, 0.0027f, 0.0029f, 0.0032f, 0.0035f,
0.0039f, 0.0044f, 0.0049f, 0.0055f, 0.0062f, 0.0072f, 0.0083f, 0.0096f,
0.0113f, 0.0135f, 0.0164f, 0.0201f, 0.0249f, 0.0314f, 0.0398f, 0.0502f,
0.0619f, 0.0718f, 0.0759f
};
static const float glorentz54[30] = {
0.0017f, 0.0018f, 0.0019f, 0.0021f, 0.0022f, 0.0024f, 0.0026f, 0.0029f,
0.0031f, 0.0034f, 0.0038f, 0.0042f, 0.0047f, 0.0052f, 0.0059f, 0.0067f,
0.0076f, 0.0088f, 0.0102f, 0.0120f, 0.0143f, 0.0171f, 0.0208f, 0.0256f,
0.0317f, 0.0395f, 0.0488f, 0.0586f, 0.0666f, 0.0698f
};
static const float glorentz55[32] = {
0.0016f, 0.0017f, 0.0018f, 0.0019f, 0.0021f, 0.0022f, 0.0024f, 0.0026f,
0.0028f, 0.0031f, 0.0034f, 0.0037f, 0.0041f, 0.0045f, 0.0050f, 0.0056f,
0.0063f, 0.0071f, 0.0081f, 0.0094f, 0.0108f, 0.0127f, 0.0149f, 0.0178f,
0.0214f, 0.0261f, 0.0318f, 0.0389f, 0.0470f, 0.0553f, 0.0618f, 0.0643f
};
static const float glorentz56[35] = {
0.0014f, 0.0015f, 0.0016f, 0.0017f, 0.0018f, 0.0020f, 0.0021f, 0.0023f,
0.0024f, 0.0026f, 0.0028f, 0.0031f, 0.0033f, 0.0036f, 0.0040f, 0.0044f,
0.0049f, 0.0054f, 0.0060f, 0.0067f, 0.0076f, 0.0087f, 0.0099f, 0.0114f,
0.0133f, 0.0156f, 0.0184f, 0.0220f, 0.0264f, 0.0318f, 0.0381f, 0.0451f,
0.0520f, 0.0572f, 0.0591f
};
static const float glorentz57[38] = {
0.0013f, 0.0014f, 0.0015f, 0.0016f, 0.0017f, 0.0018f, 0.0019f, 0.0020f,
0.0021f, 0.0023f, 0.0024f, 0.0026f, 0.0028f, 0.0031f, 0.0033f, 0.0036f,
0.0039f, 0.0043f, 0.0047f, 0.0052f, 0.0058f, 0.0064f, 0.0072f, 0.0081f,
0.0092f, 0.0104f, 0.0120f, 0.0139f, 0.0162f, 0.0190f, 0.0224f, 0.0265f,
0.0315f, 0.0371f, 0.0431f, 0.0487f, 0.0529f, 0.0544f
};
static const float glorentz58[41] = {
0.0012f, 0.0013f, 0.0014f, 0.0014f, 0.0015f, 0.0016f, 0.0017f, 0.0018f,
0.0019f, 0.0020f, 0.0022f, 0.0023f, 0.0025f, 0.0026f, 0.0028f, 0.0030f,
0.0033f, 0.0036f, 0.0039f, 0.0042f, 0.0046f, 0.0050f, 0.0056f, 0.0061f,
0.0068f, 0.0076f, 0.0086f, 0.0097f, 0.0110f, 0.0125f, 0.0144f, 0.0167f,
0.0194f, 0.0226f, 0.0265f, 0.0309f, 0.0359f, 0.0409f, 0.0455f, 0.0488f,
0.0500f
};
static const float glorentz59[45] = {
0.0011f, 0.0012f, 0.0012f, 0.0013f, 0.0013f, 0.0014f, 0.0015f, 0.0016f,
0.0016f, 0.0017f, 0.0018f, 0.0019f, 0.0021f, 0.0022f, 0.0023f, 0.0025f,
0.0026f, 0.0028f, 0.0030f, 0.0033f, 0.0035f, 0.0038f, 0.0041f, 0.0045f,
0.0049f, 0.0054f, 0.0059f, 0.0065f, 0.0072f, 0.0081f, 0.0090f, 0.0102f,
0.0115f, 0.0130f, 0.0149f, 0.0171f, 0.0197f, 0.0227f, 0.0263f, 0.0302f,
0.0345f, 0.0387f, 0.0425f, 0.0451f, 0.0460f
};
static const float glorentz60[49] = {
0.0010f, 0.0011f, 0.0011f, 0.0012f, 0.0012f, 0.0013f, 0.0013f, 0.0014f,
0.0014f, 0.0015f, 0.0016f, 0.0017f, 0.0018f, 0.0019f, 0.0020f, 0.0021f,
0.0022f, 0.0024f, 0.0025f, 0.0027f, 0.0028f, 0.0030f, 0.0033f, 0.0035f,
0.0038f, 0.0041f, 0.0044f, 0.0048f, 0.0052f, 0.0057f, 0.0063f, 0.0069f,
0.0077f, 0.0085f, 0.0095f, 0.0106f, 0.0119f, 0.0135f, 0.0153f, 0.0174f,
0.0199f, 0.0227f, 0.0259f, 0.0293f, 0.0330f, 0.0365f, 0.0395f, 0.0415f,
0.0423f
};
static const float glorentz61[53] = {
0.0009f, 0.0010f, 0.0010f, 0.0011f, 0.0011f, 0.0011f, 0.0012f, 0.0012f,
0.0013f, 0.0014f, 0.0014f, 0.0015f, 0.0016f, 0.0016f, 0.0017f, 0.0018f,
0.0019f, 0.0020f, 0.0021f, 0.0023f, 0.0024f, 0.0025f, 0.0027f, 0.0029f,
0.0031f, 0.0033f, 0.0035f, 0.0038f, 0.0041f, 0.0044f, 0.0047f, 0.0051f,
0.0056f, 0.0061f, 0.0067f, 0.0073f, 0.0081f, 0.0089f, 0.0099f, 0.0110f,
0.0124f, 0.0139f, 0.0156f, 0.0176f, 0.0199f, 0.0225f, 0.0253f, 0.0283f,
0.0314f, 0.0343f, 0.0367f, 0.0383f, 0.0389f
};
static const float glorentz62[57] = {
0.0009f, 0.0009f, 0.0009f, 0.0010f, 0.0010f, 0.0011f, 0.0011f, 0.0011f,
0.0012f, 0.0012f, 0.0013f, 0.0013f, 0.0014f, 0.0015f, 0.0015f, 0.0016f,
0.0017f, 0.0018f, 0.0019f, 0.0020f, 0.0021f, 0.0022f, 0.0023f, 0.0024f,
0.0026f, 0.0027f, 0.0029f, 0.0031f, 0.0033f, 0.0035f, 0.0038f, 0.0040f,
0.0043f, 0.0047f, 0.0050f, 0.0055f, 0.0059f, 0.0064f, 0.0070f, 0.0077f,
0.0085f, 0.0093f, 0.0103f, 0.0114f, 0.0127f, 0.0142f, 0.0158f, 0.0177f,
0.0198f, 0.0221f, 0.0246f, 0.0272f, 0.0297f, 0.0321f, 0.0340f, 0.0353f,
0.0357f
};
static const float glorentz63[62] = {
0.0008f, 0.0008f, 0.0009f, 0.0009f, 0.0009f, 0.0010f, 0.0010f, 0.0010f,
0.0011f, 0.0011f, 0.0011f, 0.0012f, 0.0012f, 0.0013f, 0.0013f, 0.0014f,
0.0015f, 0.0015f, 0.0016f, 0.0017f, 0.0017f, 0.0018f, 0.0019f, 0.0020f,
0.0021f, 0.0022f, 0.0023f, 0.0025f, 0.0026f, 0.0028f, 0.0029f, 0.0031f,
0.0033f, 0.0035f, 0.0038f, 0.0040f, 0.0043f, 0.0046f, 0.0050f, 0.0053f,
0.0058f, 0.0062f, 0.0068f, 0.0074f, 0.0081f, 0.0088f, 0.0097f, 0.0106f,
0.0117f, 0.0130f, 0.0144f, 0.0159f, 0.0176f, 0.0195f, 0.0216f, 0.0237f,
0.0259f, 0.0280f, 0.0299f, 0.0315f, 0.0325f, 0.0328f
};
static const float glorentz64[65] = {
0.0008f, 0.0008f, 0.0008f, 0.0009f, 0.0009f, 0.0009f, 0.0010f, 0.0010f,
0.0010f, 0.0011f, 0.0011f, 0.0012f, 0.0012f, 0.0012f, 0.0013f, 0.0013f,
0.0014f, 0.0014f, 0.0015f, 0.0016f, 0.0016f, 0.0017f, 0.0018f, 0.0019f,
0.0020f, 0.0021f, 0.0022f, 0.0023f, 0.0024f, 0.0025f, 0.0027f, 0.0028f,
0.0030f, 0.0031f, 0.0033f, 0.0035f, 0.0038f, 0.0040f, 0.0043f, 0.0046f,
0.0049f, 0.0052f, 0.0056f, 0.0061f, 0.0066f, 0.0071f, 0.0077f, 0.0084f,
0.0091f, 0.0100f, 0.0109f, 0.0120f, 0.0132f, 0.0145f, 0.0159f, 0.0175f,
0.0192f, 0.0209f, 0.0228f, 0.0246f, 0.0264f, 0.0279f, 0.0291f, 0.0299f,
0.0301f
};
static const float *gptr_tab_lorentz[64] = {
glorentz1, glorentz2, glorentz3, glorentz4,
glorentz5, glorentz6, glorentz7, glorentz8,
glorentz9, glorentz10, glorentz11, glorentz12,
glorentz13, glorentz14, glorentz15, glorentz16,
glorentz17, glorentz18, glorentz19, glorentz20,
glorentz21, glorentz22, glorentz23, glorentz24,
glorentz25, glorentz26, glorentz27, glorentz28,
glorentz29, glorentz30, glorentz31, glorentz32,
glorentz33, glorentz34, glorentz35, glorentz36,
glorentz37, glorentz38, glorentz39, glorentz40,
glorentz41, glorentz42, glorentz43, glorentz44,
glorentz45, glorentz46, glorentz47, glorentz48,
glorentz49, glorentz50, glorentz51, glorentz52,
glorentz53, glorentz54, glorentz55, glorentz56,
glorentz57, glorentz58, glorentz59, glorentz60,
glorentz61, glorentz62, glorentz63, glorentz64
};

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/*
main.c
QRA64 mode encode/decode tests
(c) 2016 - Nico Palermo, IV3NWV
Thanks to Andrea Montefusco IW0HDV for his help on adapting the sources
to OSs other than MS Windows
------------------------------------------------------------------------------
This file is part of the qracodes project, a Forward Error Control
encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
Files in this package:
main.c - this file
qra64.c/.h - qra64 mode encode/decoding functions
../qracodes/normrnd.{c,h} - random gaussian number generator
../qracodes/npfwht.{c,h} - Fast Walsh-Hadamard Transforms
../qracodes/pdmath.{c,h} - Elementary math on probability distributions
../qracodes/qra12_63_64_irr_b.{c,h} - Tables for a QRA(12,63) irregular RA
code over GF(64)
../qracodes/qra13_64_64_irr_e.{c,h} - Tables for a QRA(13,64) irregular RA
code over GF(64)
../qracodes/qracodes.{c,h} - QRA codes encoding/decoding functions
-------------------------------------------------------------------------------
qracodes is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
qracodes is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with qracodes source distribution.
If not, see <http://www.gnu.org/licenses/>.
-----------------------------------------------------------------------------
The code used by the QRA64 mode is the code: QRA13_64_64_IRR_E: K=13
N=64 Q=64 irregular QRA code (defined in qra13_64_64_irr_e.{h,c}).
This code has been designed to include a CRC as the 13th information
symbol and improve the code UER (Undetected Error Rate). The CRC
symbol is not sent along the channel (the codes are punctured) and the
resulting code is still a (12,63) code with an effective code rate of
R = 12/63.
*/
// OS dependent defines and includes ------------------------------------------
#if _WIN32 // note the underscore: without it, it's not msdn official!
// Windows (x64 and x86)
#include <windows.h> // required only for GetTickCount(...)
#include <process.h> // _beginthread
#endif
#if __linux__
#include <unistd.h>
#include <time.h>
unsigned GetTickCount(void) {
struct timespec ts;
unsigned theTick = 0U;
clock_gettime( CLOCK_REALTIME, &ts );
theTick = ts.tv_nsec / 1000000;
theTick += ts.tv_sec * 1000;
return theTick;
}
#endif
#if __APPLE__
#endif
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include "qra64.h"
#include "../qracodes/normrnd.h" // gaussian numbers generator
// ----------------------------------------------------------------------------
// channel types
#define CHANNEL_AWGN 0
#define CHANNEL_RAYLEIGH 1
#define CHANNEL_FASTFADE 2
#define JT65_SNR_EBNO_OFFSET 29.1f // with the synch used in JT65
#define QRA64_SNR_EBNO_OFFSET 31.0f // with the costas array synch
void printwordd(char *msg, int *x, int size)
{
int k;
printf("\n%s ",msg);
for (k=0;k<size;k++)
printf("%2d ",x[k]);
printf("\n");
}
void printwordh(char *msg, int *x, int size)
{
int k;
printf("\n%s ",msg);
for (k=0;k<size;k++)
printf("%02hx ",x[k]);
printf("\n");
}
#define NSAMPLES (QRA64_N*QRA64_M)
static float rp[NSAMPLES];
static float rq[NSAMPLES];
static float chp[NSAMPLES];
static float chq[NSAMPLES];
static float r[NSAMPLES];
float *mfskchannel(int *x, int channel_type, float EbNodB)
{
/*
Simulate an MFSK channel, either AWGN or Rayleigh.
x is a pointer to the transmitted codeword, an array of QRA64_N
integers in the range 0..63.
Returns the received symbol energies (squared amplitudes) as an array of
(QRA64_M*QRA64_N) floats. The first QRA64_M entries of this array are
the energies of the first symbol in the codeword. The second QRA64_M
entries are those of the second symbol, and so on up to the last codeword
symbol.
*/
const float No = 1.0f; // noise spectral density
const float sigma = (float)sqrt(No/2.0f); // std dev of noise I/Q components
const float sigmach = (float)sqrt(1/2.0f); // std dev of channel I/Q gains
const float R = 1.0f*QRA64_K/QRA64_N;
float EbNo = (float)pow(10,EbNodB/10);
float EsNo = 1.0f*QRA64_m*R*EbNo;
float Es = EsNo*No;
float A = (float)sqrt(Es);
int k;
normrnd_s(rp,NSAMPLES,0,sigma);
normrnd_s(rq,NSAMPLES,0,sigma);
if(EbNodB>-15)
if (channel_type == CHANNEL_AWGN)
for (k=0;k<QRA64_N;k++)
rp[k*QRA64_M+x[k]]+=A;
else
if (channel_type == CHANNEL_RAYLEIGH) {
normrnd_s(chp,QRA64_N,0,sigmach);
normrnd_s(chq,QRA64_N,0,sigmach);
for (k=0;k<QRA64_N;k++) {
rp[k*QRA64_M+x[k]]+=A*chp[k];
rq[k*QRA64_M+x[k]]+=A*chq[k];
}
}
else {
return 0; // unknown channel type
}
// compute the squares of the amplitudes of the received samples
for (k=0;k<NSAMPLES;k++)
r[k] = rp[k]*rp[k] + rq[k]*rq[k];
return r;
}
// These defines are some packed fields as computed by JT65
#define CALL_IV3NWV 0x7F85AE7
#define CALL_K1JT 0xF70DDD7
#define GRID_JN66 0x3AE4 // JN66
#define GRID_73 0x7ED0 // 73
char decode_type[12][32] = {
"[? ? ?] AP0",
"[CQ ? ?] AP27",
"[CQ ? ] AP42",
"[CALL ? ?] AP29",
"[CALL ? ] AP44",
"[CALL CALL ?] AP57",
"[? CALL ?] AP29",
"[? CALL ] AP44",
"[CALL CALL G] AP72",
"[CQ CALL ?] AP55",
"[CQ CALL ] AP70",
"[CQ CALL G] AP70"
};
char apmode_type[3][32] = {
"NO AP",
"AUTO AP",
"USER AP"
};
int test_proc_1(int channel_type, float EbNodB, int mode)
{
/*
Here we simulate the following (dummy) QSO:
1) CQ IV3NWV
2) IV3NWV K1JT
3) K1JT IV3NWV 73
4) IV3NWV K1JT 73
No message repetition is attempted
The QSO is counted as successfull if IV3NWV received the last message
When mode=QRA_AUTOAP each decoder attempts to decode the message sent
by the other station using the a-priori information derived by what
has been already decoded in a previous phase of the QSO if decoding
with no a-priori information has not been successful.
Step 1) K1JT's decoder first attempts to decode msgs of type [? ? ?]
and if this attempt fails, it attempts to decode [CQ/QRZ ? ?] or
[CQ/QRZ ?] msgs
Step 2) if IV3NWV's decoder is unable to decode K1JT's without AP it
attempts to decode messages of the type [IV3NWV ? ?] and [IV3NWV ?].
Step 3) K1JT's decoder attempts to decode [? ? ?] and [K1JT IV3NWV ?]
(this last decode type has been enabled by K1JT's encoder at step 2)
Step 4) IV3NWV's decoder attempts to decode [? ? ?] and [IV3NWV K1JT
?] (this last decode type has been enabled by IV3NWV's encoder at step
3)
At each step the simulation reports if a decode was successful. In
this case it also reports the type of decode (see table decode_type
above)
When mode=QRA_NOAP, only [? ? ?] decodes are attempted and no a-priori
information is used by the decoder
The function returns 0 if all of the four messages have been decoded
by their recipients (with no retries) and -1 if any of them could not
be decoded
*/
int x[QRA64_K], xdec[QRA64_K];
int y[QRA64_N];
float *rx;
int rc;
// Each simulated station must use its own codec since it might work with
// different a-priori information.
qra64codec *codec_iv3nwv = qra64_init(mode); // codec for IV3NWV
qra64codec *codec_k1jt = qra64_init(mode); // codec for K1JT
// Step 1a: IV3NWV makes a CQ call (with no grid)
printf("IV3NWV tx: CQ IV3NWV\n");
encodemsg_jt65(x,CALL_CQ,CALL_IV3NWV,GRID_BLANK);
qra64_encode(codec_iv3nwv, y, x);
rx = mfskchannel(y,channel_type,EbNodB);
// Step 1b: K1JT attempts to decode [? ? ?], [CQ/QRZ ? ?] or [CQ/QRZ ?]
rc = qra64_decode(codec_k1jt, 0, xdec,rx);
if (rc>=0) { // decoded
printf("K1JT rx: received with apcode=%d %s\n",rc, decode_type[rc]);
// Step 2a: K1JT replies to IV3NWV (with no grid)
printf("K1JT tx: IV3NWV K1JT\n");
encodemsg_jt65(x,CALL_IV3NWV,CALL_K1JT, GRID_BLANK);
qra64_encode(codec_k1jt, y, x);
rx = mfskchannel(y,channel_type,EbNodB);
// Step 2b: IV3NWV attempts to decode [? ? ?], [IV3NWV ? ?] or [IV3NWV ?]
rc = qra64_decode(codec_iv3nwv, 0, xdec,rx);
if (rc>=0) { // decoded
printf("IV3NWV rx: received with apcode=%d %s\n",rc, decode_type[rc]);
// Step 3a: IV3NWV replies to K1JT with a 73
printf("IV3NWV tx: K1JT IV3NWV 73\n");
encodemsg_jt65(x,CALL_K1JT,CALL_IV3NWV, GRID_73);
qra64_encode(codec_iv3nwv, y, x);
rx = mfskchannel(y,channel_type,EbNodB);
// Step 3b: K1JT attempts to decode [? ? ?] or [K1JT IV3NWV ?]
rc = qra64_decode(codec_k1jt, 0, xdec,rx);
if (rc>=0) { // decoded
printf("K1JT rx: received with apcode=%d %s\n",rc, decode_type[rc]);
// Step 4a: K1JT replies to IV3NWV with a 73
printf("K1JT tx: IV3NWV K1JT 73\n");
encodemsg_jt65(x,CALL_IV3NWV,CALL_K1JT, GRID_73);
qra64_encode(codec_k1jt, y, x);
rx = mfskchannel(y,channel_type,EbNodB);
// Step 4b: IV3NWV attempts to decode [? ? ?], [IV3NWV ? ?], or [IV3NWV ?]
rc = qra64_decode(codec_iv3nwv, 0, xdec,rx);
if (rc>=0) { // decoded
printf("IV3NWV rx: received with apcode=%d %s\n",rc, decode_type[rc]);
return 0;
}
}
}
}
printf("no decode\n");
return -1;
}
int test_proc_2(int channel_type, float EbNodB, int mode)
{
/*
Here we simulate the decoder of K1JT after K1JT has sent a msg [IV3NWV K1JT]
and IV3NWV sends him the msg [K1JT IV3NWV JN66].
If mode=QRA_NOAP, K1JT decoder attempts to decode only msgs of type [? ? ?].
If mode=QRA_AUTOP, K1JT decoder will attempt to decode also the msgs
[K1JT IV3NWV] and [K1JT IV3NWV ?].
In the case a decode is successful the return code of the qra64_decode function
indicates the amount of a-priori information required to decode the received
message according to this table:
rc=0 [? ? ?] AP0
rc=1 [CQ ? ?] AP27
rc=2 [CQ ? ] AP42
rc=3 [CALL ? ?] AP29
rc=4 [CALL ? ] AP44
rc=5 [CALL CALL ?] AP57
rc=6 [? CALL ?] AP29
rc=7 [? CALL ] AP44
rc=8 [CALL CALL GRID] AP72
rc=9 [CQ CALL ?] AP55
rc=10 [CQ CALL ] AP70
rc=11 [CQ CALL GRID] AP70
The return code is <0 when decoding is unsuccessful
This test simulates the situation ntx times and reports how many times
a particular type decode among the above 6 cases succeded.
*/
int x[QRA64_K], xdec[QRA64_K];
int y[QRA64_N];
float *rx;
float ebnodbest, ebnodbavg=0;
int rc,k;
int ndecok[12] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
int nundet = 0;
int ntx = 200,ndec=0;
qra64codec *codec_iv3nwv = qra64_init(mode); // codec for IV3NWV
qra64codec *codec_k1jt = qra64_init(mode); // codec for K1JT
printf("\nQRA64 Test #2 - Decoding with AP knowledge (SNR-Eb/No offset = %.1f dB)\n\n",
QRA64_SNR_EBNO_OFFSET);
// This will enable K1JT's decoder to look for calls directed to him [K1JT ? ?/b]
// printf("K1JT decoder enabled for [K1JT ? ?/blank]\n");
// qra64_apset(codec_k1jt, CALL_K1JT,0,0,APTYPE_MYCALL);
// This will enable K1JT's decoder to look for IV3NWV calls directed to him [K1JT IV3NWV ?/b]
// printf("K1JT decoder enabled for [K1JT IV3NWV ?]\n");
// qra64_apset(codec_k1jt, CALL_CQ,CALL_IV3NWV,0,APTYPE_BOTHCALLS);
// This will enable K1JT's decoder to look for msges sent by IV3NWV [? IV3NWV ?]
// printf("K1JT decoder enabled for [? IV3NWV ?/blank]\n");
// qra64_apset(codec_k1jt, 0,CALL_IV3NWV,GRID_BLANK,APTYPE_HISCALL);
// This will enable K1JT's decoder to look for full-knowledge [K1JT IV3NWV JN66] msgs
printf("K1JT decoder enabled for [K1JT IV3NWV JN66]\n");
qra64_apset(codec_k1jt, CALL_K1JT,CALL_IV3NWV,GRID_JN66,APTYPE_FULL);
// This will enable K1JT's decoder to look for calls from IV3NWV [CQ IV3NWV ?/b] msgs
printf("K1JT decoder enabled for [CQ IV3NWV ?/b/JN66]\n");
qra64_apset(codec_k1jt, 0,CALL_IV3NWV,GRID_JN66,APTYPE_CQHISCALL);
// Dx station IV3NWV calls
printf("\nIV3NWV encoder sends msg: [K1JT IV3NWV JN66]\n\n");
encodemsg_jt65(x,CALL_CQ,CALL_IV3NWV,GRID_JN66);
// printf("\nIV3NWV encoder sends msg: [CQ IV3NWV JN66]\n\n");
// encodemsg_jt65(x,CALL_CQ,CALL_IV3NWV,GRID_JN66);
// printf("\nIV3NWV encoder sends msg: [CQ IV3NWV]\n\n");
// encodemsg_jt65(x,CALL_CQ,CALL_IV3NWV,GRID_BLANK);
qra64_encode(codec_iv3nwv, y, x);
printf("Simulating K1JT decoder up to AP72\n");
for (k=0;k<ntx;k++) {
printf(".");
rx = mfskchannel(y,channel_type,EbNodB);
rc = qra64_decode(codec_k1jt, &ebnodbest, xdec,rx);
if (rc>=0) {
ebnodbavg +=ebnodbest;
if (memcmp(xdec,x,12*sizeof(int))==0)
ndecok[rc]++;
else
nundet++;
}
}
printf("\n\n");
printf("Transimtted msgs:%d\nDecoded msgs:\n\n",ntx);
for (k=0;k<12;k++) {
printf("%3d with %s\n",ndecok[k],decode_type[k]);
ndec += ndecok[k];
}
printf("\nTotal: %d/%d (%d undetected errors)\n\n",ndec,ntx,nundet);
printf("");
ebnodbavg/=(ndec+nundet);
printf("Estimated SNR (average in dB) = %.2f dB\n\n",ebnodbavg-QRA64_SNR_EBNO_OFFSET);
return 0;
}
int test_fastfading(float EbNodB, float B90, int fadingModel, int submode, int apmode, int olddec, int channel_type, int ntx)
{
int x[QRA64_K], xdec[QRA64_K];
int y[QRA64_N];
float *rx;
float ebnodbest, ebnodbavg=0;
int rc,k;
float rxolddec[QRA64_N*QRA64_M]; // holds the energies at nominal tone freqs
int ndecok[12] = { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
int nundet = 0;
int ndec=0;
qra64codec *codec_iv3nwv;
qra64codec *codec_k1jt;
codec_iv3nwv=qra64_init(QRA_NOAP);
codec_k1jt =qra64_init(apmode);
if (channel_type==2) { // fast-fading case
printf("Simulating the fast-fading channel\n");
printf("B90=%.2f Hz - Fading Model=%s - Submode=QRA64%c\n",B90,fadingModel?"Lorentz":"Gauss",submode+'A');
printf("Decoder metric = %s\n",olddec?"AWGN":"Matched to fast-fading signal");
}
else {
printf("Simulating the %s channel\n",channel_type?"Rayleigh block fading":"AWGN");
printf("Decoder metric = AWGN\n");
}
printf("\nEncoding msg [K1JT IV3NWV JN66]\n");
encodemsg_jt65(x,CALL_K1JT,CALL_IV3NWV,GRID_JN66);
// printf("[");
// for (k=0;k<11;k++) printf("%02hX ",x[k]); printf("%02hX]\n",x[11]);
qra64_encode(codec_iv3nwv, y, x);
printf("%d transmissions will be simulated\n\n",ntx);
if (apmode==QRA_USERAP) {
// This will enable K1JT's decoder to look for cq/qrz calls [CQ/QRZ ? ?/b]
printf("K1JT decoder enabled for [CQ ? ?/blank]\n");
qra64_apset(codec_k1jt, CALL_K1JT,0,0,APTYPE_CQQRZ);
// This will enable K1JT's decoder to look for calls directed to him [K1JT ? ?/b]
printf("K1JT decoder enabled for [K1JT ? ?/blank]\n");
qra64_apset(codec_k1jt, CALL_K1JT,0,0,APTYPE_MYCALL);
// This will enable K1JT's decoder to look for msges sent by IV3NWV [? IV3NWV ?]
printf("K1JT decoder enabled for [? IV3NWV ?/blank]\n");
qra64_apset(codec_k1jt, 0,CALL_IV3NWV,GRID_BLANK,APTYPE_HISCALL);
// This will enable K1JT's decoder to look for IV3NWV calls directed to him [K1JT IV3NWV ?/b]
printf("K1JT decoder enabled for [K1JT IV3NWV ?]\n");
qra64_apset(codec_k1jt, CALL_K1JT,CALL_IV3NWV,0,APTYPE_BOTHCALLS);
// This will enable K1JT's decoder to look for full-knowledge [K1JT IV3NWV JN66] msgs
printf("K1JT decoder enabled for [K1JT IV3NWV JN66]\n");
qra64_apset(codec_k1jt, CALL_K1JT,CALL_IV3NWV,GRID_JN66,APTYPE_FULL);
// This will enable K1JT's decoder to look for calls from IV3NWV [CQ IV3NWV ?/b] msgs
printf("K1JT decoder enabled for [CQ IV3NWV ?/b/JN66]\n");
qra64_apset(codec_k1jt, 0,CALL_IV3NWV,GRID_JN66,APTYPE_CQHISCALL);
}
printf("\nNow decoding with K1JT's decoder...\n");
/*
if (channel_type==2) // simulate a fast-faded signal
printf("Simulating a fast-fading channel with given B90 and spread type\n");
else
printf("Simulating a %s channel\n",channel_type?"Rayleigh block fading":"AWGN");
*/
for (k=0;k<ntx;k++) {
if ((k%10)==0)
printf(" %5.1f %%\r",100.0*k/ntx);
// printf("."); // work in progress
if (channel_type==2) {
// generate a fast-faded signal
rc = qra64_fastfading_channel(&rx,y,submode,EbNodB,B90,fadingModel);
if (rc<0) {
printf("\nqra64_fastfading_channel error. rc=%d\n",rc);
return -1;
}
}
else // generate a awgn or Rayleigh block fading signal
rx = mfskchannel(y, channel_type, EbNodB);
if (channel_type==2) // fast-fading case
if (olddec==1) {
int k, j;
int jj = 1<<submode;
int bps = QRA64_M*(2+jj);
float *rxbase;
float *out = rxolddec;
// calc energies at nominal freqs
for (k=0;k<QRA64_N;k++) {
rxbase = rx + QRA64_M + k*bps;
for (j=0;j<QRA64_M;j++) {
*out++=*rxbase;
rxbase+=jj;
}
}
// decode with awgn decoder
rc = qra64_decode(codec_k1jt,&ebnodbest,xdec,rxolddec);
}
else // use fast-fading decoder
rc = qra64_decode_fastfading(codec_k1jt,&ebnodbest,xdec,rx,submode,B90,fadingModel);
else // awgn or rayleigh channel. use the old decoder whatever the olddec option is
rc = qra64_decode(codec_k1jt,&ebnodbest,xdec,rx);
if (rc>=0) {
ebnodbavg +=ebnodbest;
if (memcmp(xdec,x,12*sizeof(int))==0)
ndecok[rc]++;
else {
fprintf(stderr,"\nUndetected error with rc=%d\n",rc);
nundet++;
}
}
}
printf(" %5.1f %%\r",100.0*k/ntx);
printf("\n\n");
printf("Msgs transmitted:%d\nMsg decoded:\n\n",ntx);
for (k=0;k<12;k++) {
printf("rc=%2d %3d with %s\n",k,ndecok[k],decode_type[k]);
ndec += ndecok[k];
}
printf("\nTotal: %d/%d (%d undetected errors)\n\n",ndec,ntx,nundet);
printf("");
if (ndec>0) {
ebnodbavg/=(ndec+nundet);
printf("Estimated SNR (average in dB) = %.2f dB\n\n",ebnodbavg-QRA64_SNR_EBNO_OFFSET);
}
return 0;
}
void syntax(void)
{
printf("\nQRA64 Mode Tests\n");
printf("2016, Nico Palermo - IV3NWV\n\n");
printf("---------------------------\n\n");
printf("Syntax: qra64 [-s<snrdb>] [-c<channel>] [-a<ap-type>] [-t<testtype>] [-h]\n");
printf("Options: \n");
printf(" -s<snrdb> : set simulation SNR in 2500 Hz BW (default:-27.5 dB)\n");
printf(" -c<channel> : set channel type 0=AWGN (default) 1=Rayleigh 2=Fast-fading\n");
printf(" -a<ap-type> : set decode type 0=NOAP 1=AUTOAP (default) 2=USERAP\n");
printf(" -t<testtype>: 0=simulate seq of msgs between IV3NWV and K1JT (default)\n");
printf(" 1=simulate K1JT receiving K1JT IV3NWV JN66\n");
printf(" 2=simulate fast-fading/awgn/rayliegh decoders performance\n");
printf(" -n<ntx> : simulate the transmission of ntx codewords (default=100)\n");
printf("Options used only for fast-fading simulations (-c2):\n");
printf(" -b : 90%% fading bandwidth in Hz [1..230 Hz] (default = 2.5 Hz)\n");
printf(" -m : fading model. 0=Gauss, 1=Lorentz (default = Lorentz)\n");
printf(" -q : qra64 submode. 0=QRA64A,... 4=QRA64E (default = QRA64A)\n");
printf(" -d : use the old awgn decoder\n");
printf(" -h: this help\n");
printf("Example:\n");
printf(" qra64 -t2 -c2 -a2 -b50 -m1 -q2 -n10000 -s-26\n");
printf(" runs the error performance test (-t2)\n");
printf(" with USER_AP (-a2)\n");
printf(" simulating a fast fading channel (-c2)\n");
printf(" with B90 = 50 Hz (-b50), Lorentz Doppler (-m1), mode QRA64C (-q2)\n");
printf(" ntx = 10000 codewords (-n10000) and SNR = -26 dB (-s-26)\n");
}
int main(int argc, char* argv[])
{
int k, rc, nok=0;
float SNRdB = -27.5f;
unsigned int channel = CHANNEL_AWGN;
unsigned int mode = QRA_AUTOAP;
unsigned int testtype=0;
int nqso = 100;
float EbNodB;
float B90 = 2.5;
int fadingModel = 1;
int submode = 0;
int olddec = 0;
int ntx = 100;
// Parse the command line
while(--argc) {
argv++;
if (strncmp(*argv,"-h",2)==0) {
syntax();
return 0;
}
else
if (strncmp(*argv,"-n",2)==0) {
ntx = ( int)atoi((*argv)+2);
if (ntx<100 || ntx>1000000) {
printf("Invalid -n option. ntx must be in the range [100..1000000]\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-a",2)==0) {
mode = ( int)atoi((*argv)+2);
if (mode>2) {
printf("Invalid decoding mode\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-s",2)==0) {
SNRdB = (float)atof((*argv)+2);
if (SNRdB>20 || SNRdB<-50) {
printf("SNR should be in the range [-50..20]\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-t",2)==0) {
testtype = ( int)atoi((*argv)+2);
if (testtype>2) {
printf("Invalid test type\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-c",2)==0) {
channel = ( int)atoi((*argv)+2);
if (channel>CHANNEL_FASTFADE) {
printf("Invalid channel type\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-b",2)==0) {
B90 = (float)atof((*argv)+2);
if (B90<1 || B90>230) {
printf("Invalid B90\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-m",2)==0) {
fadingModel = (int)atoi((*argv)+2);
if (fadingModel<0 || fadingModel>1) {
printf("Invalid fading model\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-q",2)==0) {
submode = (int)atoi((*argv)+2);
if (submode<0 || submode>4) {
printf("Invalid submode\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-d",2)==0) {
olddec = 1;
}
else {
printf("Invalid option\n");
syntax();
return -1;
}
}
if (testtype<2) // old tests
if (channel==CHANNEL_FASTFADE) {
printf("Invalid Option. Test type 0 and 1 supports only AWGN or Rayleigh Channel model\n");
return -1;
}
EbNodB = SNRdB+QRA64_SNR_EBNO_OFFSET;
#if defined(__linux__) || defined(__unix__)
srand48(GetTickCount());
#endif
if (testtype==0) {
for (k=0;k<nqso;k++) {
printf("\n\n------------------------\n");
rc = test_proc_1(channel, EbNodB, mode);
if (rc==0)
nok++;
}
printf("\n\n%d/%d QSOs to end without repetitions\n",nok,nqso);
printf("Input SNR = %.1fdB channel=%s ap-mode=%s\n\n",
SNRdB,
channel==CHANNEL_AWGN?"AWGN":"RAYLEIGH",
apmode_type[mode]
);
}
else if (testtype==1) {
test_proc_2(channel, EbNodB, mode);
printf("Input SNR = %.1fdB channel=%s ap-mode=%s\n\n",
SNRdB,
channel==CHANNEL_AWGN?"AWGN":"RAYLEIGH",
apmode_type[mode]
);
}
else {
printf("Input SNR = %.1fdB ap-mode=%s\n\n",
SNRdB,
apmode_type[mode]
);
test_fastfading(EbNodB,B90,fadingModel,submode,mode,olddec, channel, ntx);
}
return 0;
}

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// qra64.h
// Encoding/decoding functions for the QRA64 mode
//
// (c) 2016 - Nico Palermo, IV3NWV
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#ifndef _qra64_h_
#define _qra64_h_
// qra64_init(...) initialization flags
#define QRA_NOAP 0 // don't use a-priori knowledge
#define QRA_AUTOAP 1 // use auto a-priori knowledge
#define QRA_USERAP 2 // a-priori knowledge messages provided by the user
// QRA code parameters
#define QRA64_K 12 // information symbols
#define QRA64_N 63 // codeword length
#define QRA64_C 51 // (number of parity checks C=(N-K))
#define QRA64_M 64 // code alphabet size
#define QRA64_m 6 // bits per symbol
// packed predefined callsigns and fields as defined in JT65
#define CALL_CQ 0xFA08319
#define CALL_QRZ 0xFA0831A
#define CALL_CQ000 0xFA0831B
#define CALL_CQ999 0xFA08702
#define CALL_CQDX 0x5624C39
#define CALL_DE 0xFF641D1
#define GRID_BLANK 0x7E91
// Types of a-priori knowledge messages
#define APTYPE_CQQRZ 0 // [cq/qrz ? ?/blank]
#define APTYPE_MYCALL 1 // [mycall ? ?/blank]
#define APTYPE_HISCALL 2 // [? hiscall ?/blank]
#define APTYPE_BOTHCALLS 3 // [mycall hiscall ?]
#define APTYPE_FULL 4 // [mycall hiscall grid]
#define APTYPE_CQHISCALL 5 // [cq/qrz hiscall ?/blank]
#define APTYPE_SIZE (APTYPE_CQHISCALL+1)
typedef struct {
float decEsNoMetric;
int apflags;
int apmsg_set[APTYPE_SIZE]; // indicate which ap type knowledge has
// been set by the user
// ap messages buffers
int apmsg_cqqrz[12]; // [cq/qrz ? ?/blank]
int apmsg_call1[12]; // [mycall ? ?/blank]
int apmsg_call2[12]; // [? hiscall ?/blank]
int apmsg_call1_call2[12]; // [mycall hiscall ?]
int apmsg_call1_call2_grid[12]; // [mycall hiscall grid]
int apmsg_cq_call2[12]; // [cq hiscall ?/blank]
int apmsg_cq_call2_grid[12]; // [cq hiscall grid]
// ap messages masks
int apmask_cqqrz[12];
int apmask_cqqrz_ooo[12];
int apmask_call1[12];
int apmask_call1_ooo[12];
int apmask_call2[12];
int apmask_call2_ooo[12];
int apmask_call1_call2[12];
int apmask_call1_call2_grid[12];
int apmask_cq_call2[12];
int apmask_cq_call2_ooo[12];
} qra64codec;
#ifdef __cplusplus
extern "C" {
#endif
qra64codec *qra64_init(int flags);
// QRA64 mode initialization function
// arguments:
// flags: set the decoder mode
// QRA_NOAP use no a-priori information
// QRA_AUTOAP use any relevant previous decodes
// QRA_USERAP use a-priori information provided via qra64_apset(...)
// returns:
// Pointer to initialized qra64codec data structure
// this pointer should be passed to the encoding/decoding functions
//
// 0 if unsuccessful (can't allocate memory)
// ----------------------------------------------------------------------------
void qra64_encode(qra64codec *pcodec, int *y, const int *x);
// QRA64 encoder
// arguments:
// pcodec = pointer to a qra64codec data structure as returned by qra64_init
// x = pointer to the message to be encoded, int x[12]
// x must point to an array of integers (i.e. defined as int x[12])
// y = pointer to encoded message, int y[63]=
// ----------------------------------------------------------------------------
int qra64_decode(qra64codec *pcodec, float *ebno, int *x, const float *r);
// QRA64 mode decoder
// arguments:
// pcodec = pointer to a qra64codec data structure as returned by qra64_init
// ebno = pointer to a float where the avg Eb/No (in dB) will be stored
// in case of successfull decoding
// (pass a null pointer if not interested)
// x = pointer to decoded message, int x[12]
// r = pointer to received symbol energies (squared amplitudes)
// r must point to an array of length QRA64_M*QRA64_N (=64*63=4032)
// The first QRA_M entries should be the energies of the first
// symbol in the codeword; the last QRA_M entries should be the
// energies of the last symbol in the codeword
//
// return code:
//
// The return code is <0 when decoding is unsuccessful
// -16 indicates that the definition of QRA64_NMSG does not match what required by the code
// If the decoding process is successfull the return code is accordingly to the following table
// rc=0 [? ? ?] AP0 (decoding with no a-priori)
// rc=1 [CQ ? ?] AP27
// rc=2 [CQ ? ] AP44
// rc=3 [CALL ? ?] AP29
// rc=4 [CALL ? ] AP45
// rc=5 [CALL CALL ?] AP57
// rc=6 [? CALL ?] AP29
// rc=7 [? CALL ] AP45
// rc=8 [CALL CALL GRID] AP72 (actually a AP68 mask to reduce false decodes)
// rc=9 [CQ CALL ?] AP55
// rc=10 [CQ CALL ] AP70 (actaully a AP68 mask to reduce false decodes)
// return codes in the range 1-10 indicate the amount and the type of a-priori
// information was required to decode the received message.
// Decode a QRA64 msg using a fast-fading metric
int qra64_decode_fastfading(
qra64codec *pcodec, // ptr to the codec structure
float *ebno, // ptr to where the estimated Eb/No value will be saved
int *x, // ptr to decoded message
const float *rxen, // ptr to received symbol energies array
const int submode, // submode idx (0=QRA64A ... 4=QRA64E)
const float B90, // spread bandwidth (90% fractional energy)
const int fadingModel); // 0=Gaussian 1=Lorentzian fade model
//
// rxen: The array of the received bin energies
// Bins must be spaced by integer multiples of the symbol rate (1/Ts Hz)
// The array must be an array of total length U = L x N where:
// L: is the number of frequency bins per message symbol (see after)
// N: is the number of symbols in a QRA64 msg (63)
//
// The number of bins/symbol L depends on the selected submode accordingly to
// the following rule:
// L = (64+64*2^submode+64) = 64*(2+2^submode)
// Tone 0 is always supposed to be at offset 64 in the array.
// The m-th tone nominal frequency is located at offset 64 + m*2^submode (m=0..63)
//
// Submode A: (2^submode = 1)
// L = 64*3 = 196 bins/symbol
// Total length of the energies array: U = 192*63 = 12096 floats
//
// Submode B: (2^submode = 2)
// L = 64*4 = 256 bins/symbol
// Total length of the energies array: U = 256*63 = 16128 floats
//
// Submode C: (2^submode = 4)
// L = 64*6 = 384 bins/symbol
// Total length of the energies array: U = 384*63 = 24192 floats
//
// Submode D: (2^submode = 8)
// L = 64*10 = 640 bins/symbol
// Total length of the energies array: U = 640*63 = 40320 floats
//
// Submode E: (2^submode = 16)
// L = 64*18 = 1152 bins/symbol
// Total length of the energies array: U = 1152*63 = 72576 floats
//
// Note: The rxen array is modified and reused for internal calculations.
//
//
// B90: spread fading bandwidth in Hz (90% fractional average energy)
//
// B90 should be in the range 1 Hz ... 238 Hz
// The value passed to the call is rounded to the closest value among the
// 64 available values:
// B = 1.09^k Hz, with k=0,1,...,63
//
// I.e. B90=27 Hz will be approximated in this way:
// k = rnd(log(27)/log(1.09)) = 38
// B90 = 1.09^k = 1.09^38 = 26.4 Hz
//
// For any input value the maximum rounding error is not larger than +/- 5%
//
// return codes: same return codes of qra64_decode (+some additional error codes)
// Simulate the fast-fading channel (to be used with qra64_decode_fastfading)
int qra64_fastfading_channel(
float **rxen,
const int *xmsg,
const int submode,
const float EbN0dB,
const float B90,
const int fadingModel);
// Simulate transmission over a fading channel with given B90, fading model and submode
// and non coherent detection.
// Sets rxen to point to an array of bin energies formatted as required
// by the (fast-fading) decoding routine.
// returns 0 on success or negative values on error conditions
int qra64_apset(qra64codec *pcodec, const int mycall, const int hiscall, const int grid, const int aptype);
// Set decoder a-priori knowledge accordingly to the type of the message to
// look up for
// arguments:
// pcodec = pointer to a qra64codec data structure as returned by qra64_init
// mycall = mycall to look for
// hiscall = hiscall to look for
// grid = grid to look for
// aptype = define the type of AP to be set:
// APTYPE_CQQRZ set [cq/qrz ? ?/blank]
// APTYPE_MYCALL set [mycall ? ?/blank]
// APTYPE_HISCALL set [? hiscall ?/blank]
// APTYPE_BOTHCALLS set [mycall hiscall ?]
// APTYPE_FULL set [mycall hiscall grid]
// APTYPE_CQHISCALL set [cq/qrz hiscall ?/blank]
// returns:
// 0 on success
// -1 when qra64_init was called with the QRA_NOAP flag
// -2 invalid apytpe (valid range [APTYPE_CQQRZ..APTYPE_CQHISCALL]
// (APTYPE_CQQRZ [cq/qrz ? ?] is set by default )
void qra64_apdisable(qra64codec *pcodec, const int aptype);
// disable specific AP type
// arguments:
// pcodec = pointer to a qra64codec data structure as returned by qra64_init
// aptype = define the type of AP to be disabled
// APTYPE_CQQRZ disable [cq/qrz ? ?/blank]
// APTYPE_MYCALL disable [mycall ? ?/blank]
// APTYPE_HISCALL disable [ ? hiscall ?/blank]
// APTYPE_BOTHCALLS disable [mycall hiscall ? ]
// APTYPE_FULL disable [mycall hiscall grid]
// APTYPE_CQHISCALL set [cq/qrz hiscall ?/blank]
void qra64_close(qra64codec *pcodec);
// Free memory allocated by qra64_init
// arguments:
// pcodec = pointer to a qra64codec data structure as returned by qra64_init
// ----------------------------------------------------------------------------
// encode/decode std msgs in 12 symbols as done in jt65
void encodemsg_jt65(int *y, const int call1, const int call2, const int grid);
void decodemsg_jt65(int *call1, int *call2, int *grid, const int *x);
#ifdef __cplusplus
}
#endif
#endif // _qra64_h_

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// qra64_subs.c
// Fortran interface routines for QRA64
#include "qra64.h"
#include <stdio.h>
static qra64codec *pqra64codec = NULL;
void qra64_enc_(int x[], int y[])
{
if (pqra64codec==NULL) pqra64codec = qra64_init(QRA_USERAP);
qra64_encode(pqra64codec, y, x);
}
void qra64_dec_(float r[], int* nc1, int* nc2, int* ng2, int* APtype,
int* iset, int* ns0, float* b0, int* nf0,
int xdec[], float* snr, int* rc)
{
/*
APtype: AP
-----------------------------------------------------------------------
-1 0 (no AP information)
0 [CQ/QRZ ? ? ] 25/37
1 [MyCall ? ? ] 25/37
2 [ ? HisCall ? ] 25/37
3 [MyCall HisCall ? ] 49/68
4 [MyCall HisCall grid] 68
5 [CQ/QRZ HisCall ? ] 49/68
rc Message format AP APTYPE Comments
------------------------------------------------------------------------
-16 Failed sanity check
-2 Decoded but CRC failed
-1 No decode
0 [ ? ? ? ] 0 -1 Decode with no AP info
1 [CQ/QRZ ? ? ] 25 0
2 [CQ/QRZ ? _ ] 37 0
3 [MyCall ? ? ] 25 1
4 [MyCall ? _ ] 37 1
5 [MyCall HisCall ? ] 49 3
6 [ ? HisCall ? ] 25 2 Optional
7 [ ? HisCall _ ] 37 2 Optional
8 [MyCall HisCall Grid] 68 4
9 [CQ/QRZ HisCall ? ] 49 5 Optional (not needed?)
10 [CQ/QRZ HisCall _ ] 68 5 Optional
11 [CQ/QRZ HisCall Grid] 68 ? Optional
*/
float EbNodBEstimated;
int err=0;
int nSubmode=*ns0;
float b90=*b0;
int nFadingModel=*nf0;
if(pqra64codec==NULL) pqra64codec = qra64_init(QRA_USERAP);
err=qra64_apset(pqra64codec,*nc1,*nc2,*ng2,*APtype);
if(err<0) printf("ERROR: qra64_apset returned %d\n",err);
if(*iset==0) {
*rc = qra64_decode_fastfading(pqra64codec,&EbNodBEstimated,xdec,r,
nSubmode,b90,nFadingModel);
*snr = EbNodBEstimated - 31.0;
}
}

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$ qra64_nico -h
QRA64 Mode Tests
2016, Nico Palermo - IV3NWV
---------------------------
Syntax: qra64 [-s<snrdb>] [-c<channel>] [-a<ap-type>] [-t<testtype>] [-h]
Options:
-s<snrdb> : set simulation SNR in 2500 Hz BW (default:-27.5 dB)
-c<channel> : set channel type 0=AWGN (default) 1=Rayleigh
-a<ap-type> : set decode type 0=NOAP 1=AUTOAP (default) 2=USERAP
-t<testtype>: 0=simulate seq of msgs between IV3NWV and K1JT (default)
1=simulate K1JT receiving K1JT IV3NWV JN66
2=simulate fast-fading routines (option -c ignored)
Options used only for fast-fading simulations:
-b : 90% fading bandwidth in Hz [1..230 Hz] (default = 2.5 Hz)
-m : fading model. 0=Gauss, 1=Lorentz (default = Lorentz)
-q : qra64 submode. 0=QRA64A,... 4=QRA64E (default = QRA64A)
-h: this help
#############################################################################
Usage example:
qra64 -c2 -t2 -a2 -b50 -m1 -q2 -s-26.0 -n50000
Simulate a fast-fading channel (-c2)
Evaluate decoder performance (-t2) with
USER_AP (-a2)
B90 = 50 Hz (-b50)
Lorentz model (-m1)
submode QRA64C (-q2)
Input SNR = -26.0 dB (-s-26.0)
Simulate 50000 transmissions (-n50000)
(type qra64 -h for command syntax)
Command Output:
Input SNR = -26.0dB ap-mode=USER AP
Simulating the fast-fading channel
B90=50.00 Hz - Fading Model=Lorentz - Submode=QRA64C
Decoder metric = Matched to fast-fading signal
Encoding msg [K1JT IV3NWV JN66]
50000 transmissions will be simulated
K1JT decoder enabled for [CQ ? ?/blank]
K1JT decoder enabled for [K1JT ? ?/blank]
K1JT decoder enabled for [? IV3NWV ?/blank]
K1JT decoder enabled for [K1JT IV3NWV ?]
K1JT decoder enabled for [K1JT IV3NWV JN66]
K1JT decoder enabled for [CQ IV3NWV ?/b/JN66]
Now decoding with K1JT's decoder...
5.5 %
Undetected error with rc=6
13.1 %
Undetected error with rc=7
70.8 %
Undetected error with rc=1
75.8 %
Undetected error with rc=9
88.9 %
Undetected error with rc=6
100.0 %
Msgs transmitted:50000
Msg decoded:
rc= 0 0 with [? ? ?] AP0
rc= 1 0 with [CQ ? ?] AP27
rc= 2 0 with [CQ ? ] AP42
rc= 3 145 with [CALL ? ?] AP29
rc= 4 0 with [CALL ? ] AP44
rc= 5 12085 with [CALL CALL ?] AP57
rc= 6 0 with [? CALL ?] AP29
rc= 7 0 with [? CALL ] AP44
rc= 8 24307 with [CALL CALL G] AP72
rc= 9 0 with [CQ CALL ?] AP55
rc=10 0 with [CQ CALL ] AP70
rc=11 0 with [CQ CALL G] AP70
Total: 36537/50000 (5 undetected errors)
Estimated SNR (average in dB) = -26.26 dB

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program qra64sim
! Generate simulated QRA64 data for testing the decoder.
use wavhdr
use packjt
parameter (NMAX=54*12000) ! = 648,000
parameter (NFFT=10*65536,NH=NFFT/2)
type(hdr) h !Header for .wav file
integer*2 iwave(NMAX) !Generated waveform
integer*4 itone(84) !Channel symbols (values 0-63)
real*4 xnoise(NMAX) !Generated random noise
real*4 dat(NMAX) !Generated real data
complex cdat(NMAX) !Generated complex waveform
complex cspread(0:NFFT-1) !Complex amplitude for Rayleigh fading
complex z
real*8 f0,dt,twopi,phi,dphi,baud,fsample,freq
character msg*22,fname*11,csubmode*1,arg*12
character msgsent*22
nargs=iargc()
if(nargs.ne. 7) then
print *, 'Usage: qra64sim "msg" A-E Nsigs fDop DT Nfiles SNR'
print *, 'Example qra64sim "K1ABC W9XYZ EN37" A 10 0.2 0.0 1 0'
go to 999
endif
call getarg(1,msg)
call getarg(2,csubmode)
mode64=2**(ichar(csubmode)-ichar('A'))
call getarg(3,arg)
read(arg,*) nsigs
call getarg(4,arg)
read(arg,*) fspread
call getarg(5,arg)
read(arg,*) xdt
call getarg(6,arg)
read(arg,*) nfiles
call getarg(7,arg)
read(arg,*) snrdb
if(mode64.ge.8) nsigs=1
rms=100.
fsample=12000.d0 !Sample rate (Hz)
dt=1.d0/fsample !Sample interval (s)
twopi=8.d0*atan(1.d0)
npts=54*12000 !Total samples in .wav file
nsps=6912
baud=12000.d0/nsps !Keying rate = 1.7361111111
nsym=84 !Number of channel symbols
h=default_header(12000,npts)
dfsig=2000.0/nsigs !Freq spacing between sigs in file (Hz)
ichk=0
write(*,1000)
1000 format('File Sig Freq A-E S/N DT Dop Message'/60('-'))
do ifile=1,nfiles !Loop over requested number of files
write(fname,1002) ifile !Output filename
1002 format('000000_',i4.4)
open(10,file=fname//'.wav',access='stream',status='unknown')
xnoise=0.
cdat=0.
if(snrdb.lt.90) then
do i=1,npts
xnoise(i)=gran() !Generate gaussian noise
enddo
endif
do isig=1,nsigs !Generate requested number of sigs
if(mod(nsigs,2).eq.0) f0=1500.0 + dfsig*(isig-0.5-nsigs/2)
if(mod(nsigs,2).eq.1) f0=1500.0 + dfsig*(isig-(nsigs+1)/2)
if(nsigs.eq.1) f0=1000.0
xsnr=snrdb
if(snrdb.eq.0.0) xsnr=-20 - isig
call genqra64(msg,ichk,msgsent,itone,itype)
bandwidth_ratio=2500.0/6000.0
sig=sqrt(2*bandwidth_ratio)*10.0**(0.05*xsnr)
if(xsnr.gt.90.0) sig=1.0
write(*,1020) ifile,isig,f0,csubmode,xsnr,xdt,fspread,msg
1020 format(i4,i4,f10.3,2x,a1,2x,f5.1,f6.2,f6.1,1x,a22)
phi=0.d0
dphi=0.d0
k=(xdt+1.0)*12000 !Start audio at t = xdt + 1.0 s
isym0=-99
do i=1,npts !Add this signal into cdat()
isym=i/nsps + 1
if(isym.gt.nsym) exit
if(isym.ne.isym0) then
freq=f0 + itone(isym)*baud*mode64
dphi=twopi*freq*dt
isym0=isym
endif
phi=phi + dphi
if(phi.gt.twopi) phi=phi-twopi
xphi=phi
z=cmplx(cos(xphi),sin(xphi))
k=k+1
if(k.ge.1) cdat(k)=cdat(k) + sig*z
enddo
enddo
if(fspread.ne.0) then !Apply specified Doppler spread
df=12000.0/nfft
twopi=8*atan(1.0)
cspread(0)=1.0
cspread(NH)=0.
b=6.0 !Lorenzian 3/28 onward
do i=1,NH
f=i*df
x=b*f/fspread
z=0.
a=0.
if(x.lt.3.0) then !Cutoff beyond x=3
a=sqrt(1.111/(1.0+x*x)-0.1) !Lorentzian
call random_number(r1)
phi1=twopi*r1
z=a*cmplx(cos(phi1),sin(phi1))
endif
cspread(i)=z
z=0.
if(x.lt.50.0) then
call random_number(r2)
phi2=twopi*r2
z=a*cmplx(cos(phi2),sin(phi2))
endif
cspread(NFFT-i)=z
enddo
do i=0,NFFT-1
f=i*df
if(i.gt.NH) f=(i-nfft)*df
s=real(cspread(i))**2 + aimag(cspread(i))**2
! write(13,3000) i,f,s,cspread(i)
!3000 format(i5,f10.3,3f12.6)
enddo
! s=real(cspread(0))**2 + aimag(cspread(0))**2
! write(13,3000) 1024,0.0,s,cspread(0)
call four2a(cspread,NFFT,1,1,1) !Transform to time domain
sum=0.
do i=0,NFFT-1
p=real(cspread(i))**2 + aimag(cspread(i))**2
sum=sum+p
enddo
avep=sum/NFFT
fac=sqrt(1.0/avep)
cspread=fac*cspread !Normalize to constant avg power
cdat=cspread(1:npts)*cdat !Apply Rayleigh fading
! do i=0,NFFT-1
! p=real(cspread(i))**2 + aimag(cspread(i))**2
! write(14,3010) i,p,cspread(i)
!3010 format(i8,3f12.6)
! enddo
endif
dat=aimag(cdat) + xnoise !Add the generated noise
fac=32767.0/nsigs
if(snrdb.ge.90.0) iwave(1:npts)=nint(fac*dat(1:npts))
if(snrdb.lt.90.0) iwave(1:npts)=nint(rms*dat(1:npts))
write(10) h,iwave(1:npts) !Save the .wav file
close(10)
enddo
999 end program qra64sim

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CC = gcc
CFLAGS = -O2 -Wall -I. -D_WIN32
# Default rules
%.o: %.c
${CC} ${CFLAGS} -c $<
%.o: %.f
${FC} ${FFLAGS} -c $<
%.o: %.F
${FC} ${FFLAGS} -c $<
%.o: %.f90
${FC} ${FFLAGS} -c $<
%.o: %.F90
${FC} ${FFLAGS} -c $<
all: libqra64.a qracodes.exe
OBJS1 = normrnd.o npfwht.o pdmath.o qra12_63_64_irr_b.o \
qra13_64_64_irr_e.o qracodes.o
libqra64.a: $(OBJS1)
ar cr libqra64.a $(OBJS1)
ranlib libqra64.a
OBJS2 = main.o
qracodes.exe: $(OBJS2)
${CC} -o qracodes.exe $(OBJS2) libqra64.a -lm
.PHONY : clean
clean:
$(RM) *.o libqra64.a qracodes.exe

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# Eb/No Values to be used during the code simulation
# Each line of this file indicates the Eb/No value to be simulated (in dB)
# and the number of errors to be detected by the decoder
0.6 10000
1.1 10000
1.6 10000
2.1 10000

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# Eb/No Values to be used during the code simulation
# Each line of this file indicates the Eb/No value to be simulated (in dB)
# and the number of errors to be detected by the decoder
1.1 1000
1.6 1000
2.1 1000
2.6 1000
3.1 1000
3.6 1000
4.1 1000
4.6 1000
5.1 500
5.6 200
6.1 100
6.6 50

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# Eb/No Values to be used during the code simulation
# Each line of this file indicates the Eb/No value to be simulated (in dB)
# and the number of errors to be detected by the decoder
1.1 500
1.6 500
2.1 500
2.6 500
3.1 500
3.6 500
4.1 200
4.6 50

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// main.c
// Word Error Rate test example for Q-ary RA codes over GF(64)
//
// (c) 2016 - Nico Palermo, IV3NWV
//
// Thanks to Andrea Montefusco IW0HDV for his help on adapting the sources
// to OSs other than MS Windows
//
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// Files in this package:
// main.c - this file
// normrnd.c/.h - random gaussian number generator
// npfwht.c/.h - Fast Walsh-Hadamard Transforms
// pdmath.c/.h - Elementary math on probability distributions
// qra12_63_64_irr_b.c/.h - Tables for a QRA(12,63) irregular RA code over GF(64)
// qra13_64_64_irr_e.c/.h - Tables for a QRA(13,64) irregular RA code " "
// qracodes.c/.h - QRA codes encoding/decoding functions
//
// -------------------------------------------------------------------------------
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
// -----------------------------------------------------------------------------
// Two codes are available for simulations in this sowftware release:
// QRA12_63_64_IRR_B: K=12 N=63 Q=64 irregular QRA code (defined in qra12_63_64_irr_b.h /.c)
// QRA13_64_64_IRR_E: K=13 N=64 Q=64 irregular QRA code (defined in qra13_64_64_irr_b.h /.c)
// Codes with K=13 are designed to include a CRC as the 13th information symbol
// and improve the code UER (Undetected Error Rate).
// The CRC symbol is not sent along the channel (the codes are punctured) and the
// resulting code is still a (12,63) code with an effective code rate of R = 12/63.
// ------------------------------------------------------------------------------
// OS dependent defines and includes --------------------------------------------
#if _WIN32 // note the underscore: without it, it's not msdn official!
// Windows (x64 and x86)
#include <windows.h> // required only for GetTickCount(...)
#include <process.h> // _beginthread
#endif
#if defined(__linux__)
// remove unwanted macros
#define __cdecl
// implements Windows API
#include <time.h>
unsigned int GetTickCount(void) {
struct timespec ts;
unsigned int theTick = 0U;
clock_gettime( CLOCK_REALTIME, &ts );
theTick = ts.tv_nsec / 1000000;
theTick += ts.tv_sec * 1000;
return theTick;
}
// Convert Windows millisecond sleep
//
// VOID WINAPI Sleep(_In_ DWORD dwMilliseconds);
//
// to Posix usleep (in microseconds)
//
// int usleep(useconds_t usec);
//
#include <unistd.h>
#define Sleep(x) usleep(x*1000)
#endif
#if defined(__linux__) || ( defined(__MINGW32__) || defined (__MIGW64__) )
#include <pthread.h>
#endif
#if __APPLE__
#endif
#include <stdlib.h>
#include <stdio.h>
#include "qracodes.h"
#include "normrnd.h" // gaussian numbers generator
#include "pdmath.h" // operations on probability distributions
// defined codes
#include "qra12_63_64_irr_b.h"
#include "qra13_64_64_irr_e.h"
// -----------------------------------------------------------------------------------
#define NTHREADS_MAX 160
// channel types
#define CHANNEL_AWGN 0
#define CHANNEL_RAYLEIGH 1
// amount of a-priori information provided to the decoder
#define AP_NONE 0
#define AP_28 1
#define AP_44 2
#define AP_56 3
const char ap_str[4][16] = {
"None",
"28 bit",
"44 bit",
"56 bit"
};
const char fnameout_pfx[2][64] = {
"wer-awgn-",
"wer-rayleigh-"
};
const char fnameout_sfx[4][64] = {
"-ap00.txt",
"-ap28.txt",
"-ap44.txt",
"-ap56.txt"
};
const int ap_masks_jt65[4][13] = {
// Each row must be 13 entries long (to handle puntc. codes 13,64)
// The mask of 13th symbol (crc) is alway initializated to 0
// AP0 - no a-priori knowledge
{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
// AP28 - 1st field known [cq ? ?] or [dst ? ?]
{0x3F,0x3F,0x3F,0x3F,0x3C, 0, 0, 0, 0, 0, 0, 0},
// AP44 - 1st and 3rd fields known [cq ? 0] or [dst ? 0]
{0x3F,0x3F,0x3F,0x3F,0x3C, 0, 0, 0, 0,0x0F,0x3F,0x3F},
// AP56 - 1st and 2nd fields known [dst src ?]
{0x3F,0x3F,0x3F,0x3F,0x3F,0x3F,0x3F,0x3F,0x3F,0x30, 0, 0}
};
void ix_mask(const qracode *pcode, float *r, const int *mask, const int *x);
void printword(char *msg, int *x, int size)
{
int k;
printf("\n%s ",msg);
for (k=0;k<size;k++)
printf("%02hx ",x[k]);
printf("\n");
}
typedef struct {
int channel_type;
float EbNodB;
volatile int nt;
volatile int nerrs;
volatile int nerrsu;
volatile int stop;
volatile int done;
int ap_index; // index to the a priori knowledge mask
const qracode *pcode; // pointer to the code descriptor
int *x; //[qra_K]; input message buffer
int *y, *ydec; //[qra_N]; encoded/decoded codewords buffers
float *qra_v2cmsg; //[qra_NMSG*qra_M]; MP decoder v->c msg buffer
float *qra_c2vmsg; //[qra_NMSG*qra_M]; MP decoder c->v msg buffer
float *rp; // [qra_N*qra_M]; received samples (real component) buffer
float *rq; // [qra_N*qra_M]; received samples (imag component) buffer
float *chp; //[qra_N]; channel gains (real component) buffer
float *chq; //[qra_N]; channel gains (imag component) buffer
float *r; //[qra_N*qra_M]; received samples (amplitude) buffer
float *ix; // [qra_N*qra_M]; // intrinsic information to the MP algorithm
float *ex; // [qra_N*qra_M]; // extrinsic information from the MP algorithm
} wer_test_ds;
typedef void( __cdecl *pwer_test_thread)(wer_test_ds*);
// crc-6 generator polynomial
// g(x) = x^6 + a5*x^5 + ... + a1*x + a0
// g(x) = x^6 + x + 1
#define CRC6_GEN_POL 0x30 // MSB=a0 LSB=a5
// g(x) = x^6 + x^2 + x + 1 (as suggested by Joe. See: https://users.ece.cmu.edu/~koopman/crc/)
// #define CRC6_GEN_POL 0x38 // MSB=a0 LSB=a5. Simulation results are similar
int calc_crc6(int *x, int sz)
{
int k,j,t,sr = 0;
for (k=0;k<sz;k++) {
t = x[k];
for (j=0;j<6;j++) {
if ((t^sr)&0x01)
sr = (sr>>1) ^ CRC6_GEN_POL;
else
sr = (sr>>1);
t>>=1;
}
}
return sr;
}
void wer_test_thread(wer_test_ds *pdata)
{
const qracode *pcode=pdata->pcode;
const int qra_K = pcode->K;
const int qra_N = pcode->N;
const int qra_M = pcode->M;
const int qra_m = pcode->m;
const int NSAMPLES = pcode->N*pcode->M;
const float No = 1.0f; // noise spectral density
const float sigma = (float)sqrt(No/2.0f); // std dev of noise I/Q components
const float sigmach = (float)sqrt(1/2.0f); // std dev of channel I/Q gains
// Eb/No value for which we optimize the bessel metric
const float EbNodBMetric = 2.8f;
const float EbNoMetric = (float)pow(10,EbNodBMetric/10);
int k,t,j,diff;
float R;
float EsNoMetric;
float EbNo, EsNo, Es, A;
int channel_type, code_type;
int nt=0; // transmitted codewords
int nerrs = 0; // total number of errors
int nerrsu = 0; // number of undetected errors
int rc;
// inizialize pointer to required buffers
int *x=pdata->x; // message buffer
int *y=pdata->y, *ydec=pdata->ydec; // encoded/decoded codeword buffers
float *qra_v2cmsg=pdata->qra_v2cmsg; // table of the v->c messages
float *qra_c2vmsg=pdata->qra_c2vmsg; // table of the c->v messages
float *rp=pdata->rp; // received samples (real component)
float *rq=pdata->rq; // received samples (imag component)
float *chp=pdata->chp; // channel gains (real component)
float *chq=pdata->chq; // channel gains (imag component)
float *r=pdata->r; // received samples amplitudes
float *ix=pdata->ix; // intrinsic information to the MP algorithm
float *ex=pdata->ex; // extrinsic information from the MP algorithm
channel_type = pdata->channel_type;
code_type = pcode->type;
// define the (true) code rate accordingly to the code type
switch(code_type) {
case QRATYPE_CRC:
R = 1.0f*(qra_K-1)/qra_N;
break;
case QRATYPE_CRCPUNCTURED:
R = 1.0f*(qra_K-1)/(qra_N-1);
break;
case QRATYPE_NORMAL:
default:
R = 1.0f*(qra_K)/(qra_N);
}
EsNoMetric = 1.0f*qra_m*R*EbNoMetric;
EbNo = (float)pow(10,pdata->EbNodB/10);
EsNo = 1.0f*qra_m*R*EbNo;
Es = EsNo*No;
A = (float)sqrt(Es);
// encode the input
if (code_type==QRATYPE_CRC || code_type==QRATYPE_CRCPUNCTURED) {
// compute the information message symbol check as the (negated) xor of all the
// information message symbols
for (k=0;k<(qra_K-1);k++)
x[k]=k%qra_M;
x[k]=calc_crc6(x,qra_K-1);
}
else
for (k=0;k<qra_K;k++)
x[k]=k%qra_M;
qra_encode(pcode,y,x);
while (pdata->stop==0) {
// simulate the channel
// NOTE: in the case that the code is punctured, for simplicity
// we compute the channel outputs and the metric also for the crc symbol
// then we ignore its observation.
normrnd_s(rp,NSAMPLES,0,sigma);
normrnd_s(rq,NSAMPLES,0,sigma);
if (channel_type == CHANNEL_AWGN) {
for (k=0;k<qra_N;k++)
rp[k*qra_M+y[k]]+=A;
}
else if (channel_type == CHANNEL_RAYLEIGH) {
normrnd_s(chp,qra_N,0,sigmach);
normrnd_s(chq,qra_N,0,sigmach);
for (k=0;k<qra_N;k++) {
rp[k*qra_M+y[k]]+=A*chp[k];
rq[k*qra_M+y[k]]+=A*chq[k];
}
}
else {
pdata->done = 1;
return; // unknown channel type
}
// compute the squares of the amplitudes of the received samples
for (k=0;k<NSAMPLES;k++)
r[k] = rp[k]*rp[k] + rq[k]*rq[k];
// compute the intrinsic symbols probabilities
qra_mfskbesselmetric(ix,r,pcode->m,pcode->N,EsNoMetric);
if (code_type==QRATYPE_CRCPUNCTURED) {
// ignore observations of the CRC symbol as it is not actually sent
// over the channel
pd_init(PD_ROWADDR(ix,qra_M,qra_K),pd_uniform(qra_m),qra_M);
}
if (pdata->ap_index!=0)
// mask channel observations with a priori knowledge
ix_mask(pcode,ix,ap_masks_jt65[pdata->ap_index],x);
// compute the extrinsic symbols probabilities with the message-passing algorithm
// stop if extrinsic information does not converges to 1 within the given number of iterations
rc = qra_extrinsic(pcode,ex,ix,100,qra_v2cmsg,qra_c2vmsg);
if (rc>=0) { // the MP algorithm converged to Iex~1 in rc iterations
// decode the codeword
qra_mapdecode(pcode,ydec,ex,ix);
// look for undetected errors
if (code_type==QRATYPE_CRC || code_type==QRATYPE_CRCPUNCTURED) {
j = 0; diff = 0;
for (k=0;k<(qra_K-1);k++)
diff |= (ydec[k]!=x[k]);
t = calc_crc6(ydec,qra_K-1);
if (t!=ydec[k]) // error detected - crc doesn't matches
nerrs += 1;
else
if (diff) { // decoded message is not equal to the transmitted one but
// the crc test passed
// add as undetected error
nerrsu += 1;
nerrs += 1;
// uncomment to see what the undetected error pattern looks like
//printword("U", ydec);
}
}
else
for (k=0;k<qra_K;k++)
if (ydec[k]!=x[k]) { // decoded msg differs from the transmitted one
nerrsu += 1; // it's a false decode
nerrs += 1;
// uncomment to see what the undetected error pattern looks like
// printword("U", ydec);
break;
}
}
else // failed to converge to a solution within the given number of iterations
nerrs++;
nt = nt+1;
pdata->nt=nt;
pdata->nerrs=nerrs;
pdata->nerrsu=nerrsu;
}
pdata->done=1;
#if _WIN32
_endthread();
#endif
}
#if defined(__linux__) || ( defined(__MINGW32__) || defined (__MIGW64__) )
void *wer_test_pthread(void *p)
{
wer_test_thread ((wer_test_ds *)p);
return 0;
}
#endif
void ix_mask(const qracode *pcode, float *r, const int *mask, const int *x)
{
// mask intrinsic information (channel observations) with a priori knowledge
int k,kk, smask;
const int qra_K=pcode->K;
const int qra_M=pcode->M;
const int qra_m=pcode->m;
for (k=0;k<qra_K;k++) {
smask = mask[k];
if (smask) {
for (kk=0;kk<qra_M;kk++)
if (((kk^x[k])&smask)!=0)
*(PD_ROWADDR(r,qra_M,k)+kk) = 0.f;
pd_norm(PD_ROWADDR(r,qra_M,k),qra_m);
}
}
}
int wer_test_proc(const qracode *pcode, int nthreads, int chtype, int ap_index, float *EbNodB, int *nerrstgt, int nitems)
{
int k,nn,j,nt,nerrs,nerrsu,nd;
int cini,cend;
char fnameout[128];
FILE *fout;
wer_test_ds wt[NTHREADS_MAX];
float pe,avgt;
nn = sizeof(EbNodB)/sizeof(float); // size of the EbNo array to test
if (nthreads>NTHREADS_MAX) {
printf("Error: nthreads should be <=%d\n",NTHREADS_MAX);
return -1;
}
sprintf(fnameout,"%s%s%s",
fnameout_pfx[chtype],
pcode->name,
fnameout_sfx[ap_index]);
fout = fopen(fnameout,"w");
fprintf(fout,"# Channel (0=AWGN,1=Rayleigh), Eb/No (dB), Transmitted codewords, Errors, Undetected Errors, Avg dec. time (ms), WER\n");
printf("\nTesting the code %s over the %s channel\nSimulation data will be saved to %s\n",
pcode->name,
chtype==CHANNEL_AWGN?"AWGN":"Rayleigh",
fnameout);
fflush (stdout);
// init fixed thread parameters and preallocate buffers
for (j=0;j<nthreads;j++) {
wt[j].channel_type=chtype;
wt[j].ap_index = ap_index;
wt[j].pcode = pcode;
wt[j].x = (int*)malloc(pcode->K*sizeof(int));
wt[j].y = (int*)malloc(pcode->N*sizeof(int));
wt[j].ydec = (int*)malloc(pcode->N*sizeof(int));
wt[j].qra_v2cmsg = (float*)malloc(pcode->NMSG*pcode->M*sizeof(float));
wt[j].qra_c2vmsg = (float*)malloc(pcode->NMSG*pcode->M*sizeof(float));
wt[j].rp = (float*)malloc(pcode->N*pcode->M*sizeof(float));
wt[j].rq = (float*)malloc(pcode->N*pcode->M*sizeof(float));
wt[j].chp = (float*)malloc(pcode->N*sizeof(float));
wt[j].chq = (float*)malloc(pcode->N*sizeof(float));
wt[j].r = (float*)malloc(pcode->N*pcode->M*sizeof(float));
wt[j].ix = (float*)malloc(pcode->N*pcode->M*sizeof(float));
wt[j].ex = (float*)malloc(pcode->N*pcode->M*sizeof(float));
}
for (k=0;k<nitems;k++) {
printf("\nTesting at Eb/No=%4.1f dB...",EbNodB[k]);
fflush (stdout);
for (j=0;j<nthreads;j++) {
wt[j].EbNodB=EbNodB[k];
wt[j].nt=0;
wt[j].nerrs=0;
wt[j].nerrsu=0;
wt[j].done = 0;
wt[j].stop = 0;
#if defined(__linux__) || ( defined(__MINGW32__) || defined (__MIGW64__) )
if (pthread_create (&wt[j].thread, 0, wer_test_pthread, &wt[j])) {
perror ("Creating thread: ");
exit (255);
}
#else
_beginthread((void*)(void*)wer_test_thread,0,&wt[j]);
#endif
}
nd = 0;
cini = GetTickCount();
while (1) {
// count errors
nerrs = 0;
for (j=0;j<nthreads;j++)
nerrs += wt[j].nerrs;
// stop the working threads
// if number of errors reached at this Eb/No value
if (nerrs>=nerrstgt[k]) {
for (j=0;j<nthreads;j++)
wt[j].stop = 1;
break;
}
else { // continue with the simulation
Sleep(2);
nd = (nd+1)%100;
if (nd==0) {
printf(".");
fflush (stdout);
}
}
}
cend = GetTickCount();
// wait for the working threads to exit
for (j=0;j<nthreads;j++)
#if defined(__linux__) || ( defined(__MINGW32__) || defined (__MIGW64__) )
{
void *rc;
if (pthread_join (wt[j].thread, &rc)) {
perror ("Waiting working threads to exit");
exit (255);
}
}
#else
while(wt[j].done==0)
Sleep(1);
#endif
printf("\n");
fflush (stdout);
// compute the total number of transmitted codewords
// the total number of errors and the total number of undetected errors
nt = 0;
nerrs =0;
nerrsu = 0;
for (j=0;j<nthreads;j++) {
nt += wt[j].nt;
nerrs += wt[j].nerrs;
nerrsu += wt[j].nerrsu;
}
pe = 1.0f*nerrs/nt; // word error rate
avgt = 1.0f*(cend-cini)/nt; // average time per decode (ms)
printf("Elapsed Time=%6.1fs (%5.2fms/word)\nTransmitted=%8d - Errors=%6d - Undetected=%3d - WER=%.2e\n",
0.001f*(cend-cini),
avgt, nt, nerrs, nerrsu, pe);
fflush (stdout);
// save simulation data to output file
fprintf(fout,"%01d %.2f %d %d %d %.2f %.2e\n",
chtype,
EbNodB[k],
nt,
nerrs,
nerrsu,
avgt,
pe);
}
fclose(fout);
return 0;
}
const qracode *codetotest[] = {
&qra_12_63_64_irr_b,
&qra_13_64_64_irr_e
};
void syntax(void)
{
printf("\nQ-ary Repeat-Accumulate Code Word Error Rate Simulator\n");
printf("2016, Nico Palermo - IV3NWV\n\n");
printf("Syntax: qracodes [-q<code_index>] [-t<threads>] [-c<ch_type>] [-a<ap_index>] [-f<fnamein>[-h]\n");
printf("Options: \n");
printf(" -q<code_index>: code to simulate. 0=qra_12_63_64_irr_b\n");
printf(" 1=qra_13_64_64_irr_e (default)\n");
printf(" -t<threads> : number of threads to be used for the simulation [1..24]\n");
printf(" (default=8)\n");
printf(" -c<ch_type> : channel_type. 0=AWGN 1=Rayleigh \n");
printf(" (default=AWGN)\n");
printf(" -a<ap_index> : amount of a-priori information provided to decoder. \n");
printf(" 0= No a-priori (default)\n");
printf(" 1= 28 bit \n");
printf(" 2= 44 bit \n");
printf(" 3= 56 bit \n");
printf(" -f<fnamein> : name of the file containing the Eb/No values to be simulated\n");
printf(" (default=ebnovalues.txt)\n");
printf(" This file should contain lines in this format:\n");
printf(" # Eb/No(dB) Target Errors\n");
printf(" 0.1 5000\n");
printf(" 0.6 5000\n");
printf(" 1.1 1000\n");
printf(" 1.6 1000\n");
printf(" ...\n");
printf(" (lines beginning with a # are treated as comments\n\n");
}
#define SIM_POINTS_MAX 20
int main(int argc, char* argv[])
{
float EbNodB[SIM_POINTS_MAX];
int nerrstgt[SIM_POINTS_MAX];
FILE *fin;
char fnamein[128]= "ebnovalues.txt";
char buf[128];
int nitems = 0;
int code_idx = 1;
int nthreads = 8;
int ch_type = CHANNEL_AWGN;
int ap_index = AP_NONE;
// parse command line
while(--argc) {
argv++;
if (strncmp(*argv,"-h",2)==0) {
syntax();
return 0;
}
else
if (strncmp(*argv,"-q",2)==0) {
code_idx = (int)atoi((*argv)+2);
if (code_idx>1) {
printf("Invalid code index\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-t",2)==0) {
nthreads = (int)atoi((*argv)+2);
printf("nthreads = %d\n",nthreads);
if (nthreads>NTHREADS_MAX) {
printf("Invalid number of threads\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-c",2)==0) {
ch_type = (int)atoi((*argv)+2);
if (ch_type>CHANNEL_RAYLEIGH) {
printf("Invalid channel type\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-a",2)==0) {
ap_index = (int)atoi((*argv)+2);
if (ap_index>AP_56) {
printf("Invalid a-priori information index\n");
syntax();
return -1;
}
}
else
if (strncmp(*argv,"-f",2)==0) {
strncpy(fnamein,(*argv)+2,127);
}
else
if (strncmp(*argv,"-h",2)==0) {
syntax();
return -1;
}
else {
printf("Invalid option\n");
syntax();
return -1;
}
}
// parse points to be simulated from the input file
fin = fopen(fnamein,"r");
if (!fin) {
printf("Can't open file: %s\n",fnamein);
syntax();
}
while (fgets(buf,128,fin)!=0)
if (*buf=='#' || *buf=='\n' )
continue;
else
if (nitems==SIM_POINTS_MAX)
break;
else
if (sscanf(buf,"%f %u",&EbNodB[nitems],&nerrstgt[nitems])!=2) {
printf("Invalid input file format\n");
syntax();
return -1;
}
else
nitems++;
fclose(fin);
if (nitems==0) {
printf("No Eb/No point specified in file %s\n",fnamein);
syntax();
return -1;
}
printf("\nQ-ary Repeat-Accumulate Code Word Error Rate Simulator\n");
printf("2016, Nico Palermo - IV3NWV\n\n");
printf("Nthreads = %d\n",nthreads);
printf("Channel = %s\n",ch_type==CHANNEL_AWGN?"AWGN":"Rayleigh");
printf("Codename = %s\n",codetotest[code_idx]->name);
printf("A-priori = %s\n",ap_str[ap_index]);
printf("Eb/No input file = %s\n\n",fnamein);
wer_test_proc(codetotest[code_idx], nthreads, ch_type, ap_index, EbNodB, nerrstgt, nitems);
return 0;
}

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// normrnd.c
// functions to generate gaussian distributed numbers
//
// (c) 2016 - Nico Palermo, IV3NWV - Microtelecom Srl, Italy
//
// Credits to Andrea Montefusco - IW0HDV for his help on adapting the sources
// to OSs other than MS Windows
//
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#include "normrnd.h"
#if _WIN32 // note the underscore: without it, it's not msdn official!
// Windows (x64 and x86)
#include <windows.h> // required only for GetTickCount(...)
#define K_RAND_MAX UINT_MAX
#elif _SVID_SOURCE || _XOPEN_SOURCE || __unix__ || (defined (__APPLE__) && defined(__MACH__)) /* POSIX or Unix or Apple */
#include <stdlib.h>
#define rand_s(x) (*x)=(unsigned int)lrand48() // returns unsigned integers in the range 0..0x7FFFFFFF
#define K_RAND_MAX 0x7FFFFFFF // that's the max number
// generated by lrand48
#else
#error "No good quality PRNG found"
#endif
// use MS rand_s(...) function
void normrnd_s(float *dst, int nitems, float mean, float stdev)
{
unsigned int r;
float phi=0, u=0;
int set = 0;
while (nitems--)
if (set==1) {
*dst++ = (float)sin(phi)*u*stdev+mean;
set = 0;
}
else {
rand_s((unsigned int*)&r); phi = (M_2PI/(1.0f+K_RAND_MAX))*r;
rand_s((unsigned int*)&r); u = (float)sqrt(-2.0f* log( (1.0f/(1.0f+K_RAND_MAX))*(1.0f+r) ) );
*dst++ = (float)cos(phi)*u*stdev+mean;
set=1;
}
}
/* NOT USED
// use MS rand() function
void normrnd(float *dst, int nitems, float mean, float stdev)
{
float phi=0, u=0;
int set = 0;
while (nitems--)
if (set==1) {
*dst++ = (float)sin(phi)*u*stdev+mean;
set = 0;
}
else {
phi = (M_2PI/(1.0f+RAND_MAX))*rand();
u = (float)sqrt(-2.0f* log( (1.0f/(1.0f+RAND_MAX))*(1.0f+rand()) ) );
*dst++ = (float)cos(phi)*u*stdev+mean;
set=1;
}
}
*/

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// normrnd.h
// Functions to generate gaussian distributed numbers
//
// (c) 2016 - Nico Palermo, IV3NWV - Microtelecom Srl, Italy
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#ifndef _normrnd_h_
#define _normrnd_h_
#define _CRT_RAND_S
#include <stdlib.h>
#define _USE_MATH_DEFINES
#include <math.h>
#define M_2PI (2.0f*(float)M_PI)
#ifdef __cplusplus
extern "C" {
#endif
void normrnd_s(float *dst, int nitems, float mean, float stdev);
// generate a random array of numbers with a gaussian distribution of given mean and stdev
// use MS rand_s(...) function
/* not used
void normrnd(float *dst, int nitems, float mean, float stdev);
// generate a random array of numbers with a gaussian distribution of given mean and stdev
// use MS rand() function
*/
#ifdef __cplusplus
}
#endif
#endif // _normrnd_h_

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// npfwht.c
// Basic implementation of the Fast Walsh-Hadamard Transforms
//
// (c) 2016 - Nico Palermo, IV3NWV - Microtelecom Srl, Italy
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (repeat and accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#include "npfwht.h"
#define WHBFY(dst,src,base,offs,dist) { dst[base+offs]=src[base+offs]+src[base+offs+dist]; dst[base+offs+dist]=src[base+offs]-src[base+offs+dist]; }
typedef void (*pnp_fwht)(float*,float*);
static void np_fwht2(float *dst, float *src);
static void np_fwht1(float *dst, float *src);
static void np_fwht2(float *dst, float *src);
static void np_fwht4(float *dst, float *src);
static void np_fwht8(float *dst, float *src);
static void np_fwht16(float *dst, float *src);
static void np_fwht32(float *dst, float *src);
static void np_fwht64(float *dst, float *src);
static pnp_fwht np_fwht_tab[7] = {
np_fwht1,
np_fwht2,
np_fwht4,
np_fwht8,
np_fwht16,
np_fwht32,
np_fwht64
};
void np_fwht(int nlogdim, float *dst, float *src)
{
np_fwht_tab[nlogdim](dst,src);
}
static void np_fwht1(float *dst, float *src)
{
dst[0] = src[0];
}
static void np_fwht2(float *dst, float *src)
{
float t[2];
WHBFY(t,src,0,0,1);
dst[0]= t[0];
dst[1]= t[1];
}
static void np_fwht4(float *dst, float *src)
{
float t[4];
// group 1
WHBFY(t,src,0,0,2); WHBFY(t,src,0,1,2);
// group 2
WHBFY(dst,t,0,0,1); WHBFY(dst,t,2,0,1);
};
static void np_fwht8(float *dst, float *src)
{
float t[16];
float *t1=t, *t2=t+8;
// group 1
WHBFY(t1,src,0,0,4); WHBFY(t1,src,0,1,4); WHBFY(t1,src,0,2,4); WHBFY(t1,src,0,3,4);
// group 2
WHBFY(t2,t1,0,0,2); WHBFY(t2,t1,0,1,2); WHBFY(t2,t1,4,0,2); WHBFY(t2,t1,4,1,2);
// group 3
WHBFY(dst,t2,0,0,1); WHBFY(dst,t2,2,0,1); WHBFY(dst,t2,4,0,1); WHBFY(dst,t2,6,0,1);
};
static void np_fwht16(float *dst, float *src)
{
float t[32];
float *t1=t, *t2=t+16;
// group 1
WHBFY(t1,src,0,0,8); WHBFY(t1,src,0,1,8); WHBFY(t1,src,0,2,8); WHBFY(t1,src,0,3,8);
WHBFY(t1,src,0,4,8); WHBFY(t1,src,0,5,8); WHBFY(t1,src,0,6,8); WHBFY(t1,src,0,7,8);
// group 2
WHBFY(t2,t1,0,0,4); WHBFY(t2,t1,0,1,4); WHBFY(t2,t1,0,2,4); WHBFY(t2,t1,0,3,4);
WHBFY(t2,t1,8,0,4); WHBFY(t2,t1,8,1,4); WHBFY(t2,t1,8,2,4); WHBFY(t2,t1,8,3,4);
// group 3
WHBFY(t1,t2,0,0,2); WHBFY(t1,t2,0,1,2); WHBFY(t1,t2,4,0,2); WHBFY(t1,t2,4,1,2);
WHBFY(t1,t2,8,0,2); WHBFY(t1,t2,8,1,2); WHBFY(t1,t2,12,0,2); WHBFY(t1,t2,12,1,2);
// group 4
WHBFY(dst,t1,0,0,1); WHBFY(dst,t1,2,0,1); WHBFY(dst,t1,4,0,1); WHBFY(dst,t1,6,0,1);
WHBFY(dst,t1,8,0,1); WHBFY(dst,t1,10,0,1); WHBFY(dst,t1,12,0,1); WHBFY(dst,t1,14,0,1);
}
static void np_fwht32(float *dst, float *src)
{
float t[64];
float *t1=t, *t2=t+32;
// group 1
WHBFY(t1,src,0,0,16); WHBFY(t1,src,0,1,16); WHBFY(t1,src,0,2,16); WHBFY(t1,src,0,3,16);
WHBFY(t1,src,0,4,16); WHBFY(t1,src,0,5,16); WHBFY(t1,src,0,6,16); WHBFY(t1,src,0,7,16);
WHBFY(t1,src,0,8,16); WHBFY(t1,src,0,9,16); WHBFY(t1,src,0,10,16); WHBFY(t1,src,0,11,16);
WHBFY(t1,src,0,12,16); WHBFY(t1,src,0,13,16); WHBFY(t1,src,0,14,16); WHBFY(t1,src,0,15,16);
// group 2
WHBFY(t2,t1,0,0,8); WHBFY(t2,t1,0,1,8); WHBFY(t2,t1,0,2,8); WHBFY(t2,t1,0,3,8);
WHBFY(t2,t1,0,4,8); WHBFY(t2,t1,0,5,8); WHBFY(t2,t1,0,6,8); WHBFY(t2,t1,0,7,8);
WHBFY(t2,t1,16,0,8); WHBFY(t2,t1,16,1,8); WHBFY(t2,t1,16,2,8); WHBFY(t2,t1,16,3,8);
WHBFY(t2,t1,16,4,8); WHBFY(t2,t1,16,5,8); WHBFY(t2,t1,16,6,8); WHBFY(t2,t1,16,7,8);
// group 3
WHBFY(t1,t2,0,0,4); WHBFY(t1,t2,0,1,4); WHBFY(t1,t2,0,2,4); WHBFY(t1,t2,0,3,4);
WHBFY(t1,t2,8,0,4); WHBFY(t1,t2,8,1,4); WHBFY(t1,t2,8,2,4); WHBFY(t1,t2,8,3,4);
WHBFY(t1,t2,16,0,4); WHBFY(t1,t2,16,1,4); WHBFY(t1,t2,16,2,4); WHBFY(t1,t2,16,3,4);
WHBFY(t1,t2,24,0,4); WHBFY(t1,t2,24,1,4); WHBFY(t1,t2,24,2,4); WHBFY(t1,t2,24,3,4);
// group 4
WHBFY(t2,t1,0,0,2); WHBFY(t2,t1,0,1,2); WHBFY(t2,t1,4,0,2); WHBFY(t2,t1,4,1,2);
WHBFY(t2,t1,8,0,2); WHBFY(t2,t1,8,1,2); WHBFY(t2,t1,12,0,2); WHBFY(t2,t1,12,1,2);
WHBFY(t2,t1,16,0,2); WHBFY(t2,t1,16,1,2); WHBFY(t2,t1,20,0,2); WHBFY(t2,t1,20,1,2);
WHBFY(t2,t1,24,0,2); WHBFY(t2,t1,24,1,2); WHBFY(t2,t1,28,0,2); WHBFY(t2,t1,28,1,2);
// group 5
WHBFY(dst,t2,0,0,1); WHBFY(dst,t2,2,0,1); WHBFY(dst,t2,4,0,1); WHBFY(dst,t2,6,0,1);
WHBFY(dst,t2,8,0,1); WHBFY(dst,t2,10,0,1); WHBFY(dst,t2,12,0,1); WHBFY(dst,t2,14,0,1);
WHBFY(dst,t2,16,0,1); WHBFY(dst,t2,18,0,1); WHBFY(dst,t2,20,0,1); WHBFY(dst,t2,22,0,1);
WHBFY(dst,t2,24,0,1); WHBFY(dst,t2,26,0,1); WHBFY(dst,t2,28,0,1); WHBFY(dst,t2,30,0,1);
}
static void np_fwht64(float *dst, float *src)
{
float t[128];
float *t1=t, *t2=t+64;
// group 1
WHBFY(t1,src,0,0,32); WHBFY(t1,src,0,1,32); WHBFY(t1,src,0,2,32); WHBFY(t1,src,0,3,32);
WHBFY(t1,src,0,4,32); WHBFY(t1,src,0,5,32); WHBFY(t1,src,0,6,32); WHBFY(t1,src,0,7,32);
WHBFY(t1,src,0,8,32); WHBFY(t1,src,0,9,32); WHBFY(t1,src,0,10,32); WHBFY(t1,src,0,11,32);
WHBFY(t1,src,0,12,32); WHBFY(t1,src,0,13,32); WHBFY(t1,src,0,14,32); WHBFY(t1,src,0,15,32);
WHBFY(t1,src,0,16,32); WHBFY(t1,src,0,17,32); WHBFY(t1,src,0,18,32); WHBFY(t1,src,0,19,32);
WHBFY(t1,src,0,20,32); WHBFY(t1,src,0,21,32); WHBFY(t1,src,0,22,32); WHBFY(t1,src,0,23,32);
WHBFY(t1,src,0,24,32); WHBFY(t1,src,0,25,32); WHBFY(t1,src,0,26,32); WHBFY(t1,src,0,27,32);
WHBFY(t1,src,0,28,32); WHBFY(t1,src,0,29,32); WHBFY(t1,src,0,30,32); WHBFY(t1,src,0,31,32);
// group 2
WHBFY(t2,t1,0,0,16); WHBFY(t2,t1,0,1,16); WHBFY(t2,t1,0,2,16); WHBFY(t2,t1,0,3,16);
WHBFY(t2,t1,0,4,16); WHBFY(t2,t1,0,5,16); WHBFY(t2,t1,0,6,16); WHBFY(t2,t1,0,7,16);
WHBFY(t2,t1,0,8,16); WHBFY(t2,t1,0,9,16); WHBFY(t2,t1,0,10,16); WHBFY(t2,t1,0,11,16);
WHBFY(t2,t1,0,12,16); WHBFY(t2,t1,0,13,16); WHBFY(t2,t1,0,14,16); WHBFY(t2,t1,0,15,16);
WHBFY(t2,t1,32,0,16); WHBFY(t2,t1,32,1,16); WHBFY(t2,t1,32,2,16); WHBFY(t2,t1,32,3,16);
WHBFY(t2,t1,32,4,16); WHBFY(t2,t1,32,5,16); WHBFY(t2,t1,32,6,16); WHBFY(t2,t1,32,7,16);
WHBFY(t2,t1,32,8,16); WHBFY(t2,t1,32,9,16); WHBFY(t2,t1,32,10,16); WHBFY(t2,t1,32,11,16);
WHBFY(t2,t1,32,12,16); WHBFY(t2,t1,32,13,16); WHBFY(t2,t1,32,14,16); WHBFY(t2,t1,32,15,16);
// group 3
WHBFY(t1,t2,0,0,8); WHBFY(t1,t2,0,1,8); WHBFY(t1,t2,0,2,8); WHBFY(t1,t2,0,3,8);
WHBFY(t1,t2,0,4,8); WHBFY(t1,t2,0,5,8); WHBFY(t1,t2,0,6,8); WHBFY(t1,t2,0,7,8);
WHBFY(t1,t2,16,0,8); WHBFY(t1,t2,16,1,8); WHBFY(t1,t2,16,2,8); WHBFY(t1,t2,16,3,8);
WHBFY(t1,t2,16,4,8); WHBFY(t1,t2,16,5,8); WHBFY(t1,t2,16,6,8); WHBFY(t1,t2,16,7,8);
WHBFY(t1,t2,32,0,8); WHBFY(t1,t2,32,1,8); WHBFY(t1,t2,32,2,8); WHBFY(t1,t2,32,3,8);
WHBFY(t1,t2,32,4,8); WHBFY(t1,t2,32,5,8); WHBFY(t1,t2,32,6,8); WHBFY(t1,t2,32,7,8);
WHBFY(t1,t2,48,0,8); WHBFY(t1,t2,48,1,8); WHBFY(t1,t2,48,2,8); WHBFY(t1,t2,48,3,8);
WHBFY(t1,t2,48,4,8); WHBFY(t1,t2,48,5,8); WHBFY(t1,t2,48,6,8); WHBFY(t1,t2,48,7,8);
// group 4
WHBFY(t2,t1,0,0,4); WHBFY(t2,t1,0,1,4); WHBFY(t2,t1,0,2,4); WHBFY(t2,t1,0,3,4);
WHBFY(t2,t1,8,0,4); WHBFY(t2,t1,8,1,4); WHBFY(t2,t1,8,2,4); WHBFY(t2,t1,8,3,4);
WHBFY(t2,t1,16,0,4); WHBFY(t2,t1,16,1,4); WHBFY(t2,t1,16,2,4); WHBFY(t2,t1,16,3,4);
WHBFY(t2,t1,24,0,4); WHBFY(t2,t1,24,1,4); WHBFY(t2,t1,24,2,4); WHBFY(t2,t1,24,3,4);
WHBFY(t2,t1,32,0,4); WHBFY(t2,t1,32,1,4); WHBFY(t2,t1,32,2,4); WHBFY(t2,t1,32,3,4);
WHBFY(t2,t1,40,0,4); WHBFY(t2,t1,40,1,4); WHBFY(t2,t1,40,2,4); WHBFY(t2,t1,40,3,4);
WHBFY(t2,t1,48,0,4); WHBFY(t2,t1,48,1,4); WHBFY(t2,t1,48,2,4); WHBFY(t2,t1,48,3,4);
WHBFY(t2,t1,56,0,4); WHBFY(t2,t1,56,1,4); WHBFY(t2,t1,56,2,4); WHBFY(t2,t1,56,3,4);
// group 5
WHBFY(t1,t2,0,0,2); WHBFY(t1,t2,0,1,2); WHBFY(t1,t2,4,0,2); WHBFY(t1,t2,4,1,2);
WHBFY(t1,t2,8,0,2); WHBFY(t1,t2,8,1,2); WHBFY(t1,t2,12,0,2); WHBFY(t1,t2,12,1,2);
WHBFY(t1,t2,16,0,2); WHBFY(t1,t2,16,1,2); WHBFY(t1,t2,20,0,2); WHBFY(t1,t2,20,1,2);
WHBFY(t1,t2,24,0,2); WHBFY(t1,t2,24,1,2); WHBFY(t1,t2,28,0,2); WHBFY(t1,t2,28,1,2);
WHBFY(t1,t2,32,0,2); WHBFY(t1,t2,32,1,2); WHBFY(t1,t2,36,0,2); WHBFY(t1,t2,36,1,2);
WHBFY(t1,t2,40,0,2); WHBFY(t1,t2,40,1,2); WHBFY(t1,t2,44,0,2); WHBFY(t1,t2,44,1,2);
WHBFY(t1,t2,48,0,2); WHBFY(t1,t2,48,1,2); WHBFY(t1,t2,52,0,2); WHBFY(t1,t2,52,1,2);
WHBFY(t1,t2,56,0,2); WHBFY(t1,t2,56,1,2); WHBFY(t1,t2,60,0,2); WHBFY(t1,t2,60,1,2);
// group 6
WHBFY(dst,t1,0,0,1); WHBFY(dst,t1,2,0,1); WHBFY(dst,t1,4,0,1); WHBFY(dst,t1,6,0,1);
WHBFY(dst,t1,8,0,1); WHBFY(dst,t1,10,0,1); WHBFY(dst,t1,12,0,1); WHBFY(dst,t1,14,0,1);
WHBFY(dst,t1,16,0,1); WHBFY(dst,t1,18,0,1); WHBFY(dst,t1,20,0,1); WHBFY(dst,t1,22,0,1);
WHBFY(dst,t1,24,0,1); WHBFY(dst,t1,26,0,1); WHBFY(dst,t1,28,0,1); WHBFY(dst,t1,30,0,1);
WHBFY(dst,t1,32,0,1); WHBFY(dst,t1,34,0,1); WHBFY(dst,t1,36,0,1); WHBFY(dst,t1,38,0,1);
WHBFY(dst,t1,40,0,1); WHBFY(dst,t1,42,0,1); WHBFY(dst,t1,44,0,1); WHBFY(dst,t1,46,0,1);
WHBFY(dst,t1,48,0,1); WHBFY(dst,t1,50,0,1); WHBFY(dst,t1,52,0,1); WHBFY(dst,t1,54,0,1);
WHBFY(dst,t1,56,0,1); WHBFY(dst,t1,58,0,1); WHBFY(dst,t1,60,0,1); WHBFY(dst,t1,62,0,1);
}

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// np_fwht.h
// Basic implementation of the Fast Walsh-Hadamard Transforms
//
// (c) 2016 - Nico Palermo, IV3NWV - Microtelecom Srl, Italy
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (repeat and accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#ifndef _npfwht_h_
#define _npfwht_h_
#ifdef __cplusplus
extern "C" {
#endif
void np_fwht(int nlogdim, float *dst, float *src);
// Compute the Walsh-Hadamard transform of the given data up to a
// 64-dimensional transform
//
// Input parameters:
// nlogdim: log2 of the transform size. Must be in the range [0..6]
// src : pointer to the input data buffer.
// dst : pointer to the output data buffer.
//
// src and dst must point to preallocated data buffers of size 2^nlogdim*sizeof(float)
// src and dst buffers can overlap
#ifdef __cplusplus
}
#endif
#endif // _npfwht_

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// pdmath.c
// Elementary math on probability distributions
//
// (c) 2016 - Nico Palermo, IV3NWV - Microtelecom Srl, Italy
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#include "pdmath.h"
typedef const float *ppd_uniform;
typedef void (*ppd_imul)(float*,const float*);
typedef float (*ppd_norm)(float*);
// define vector size in function of its logarithm in base 2
static const int pd_log2dim[7] = {
1,2,4,8,16,32,64
};
// define uniform distributions of given size
static const float pd_uniform1[1] = {
1.
};
static const float pd_uniform2[2] = {
1./2., 1./2.
};
static const float pd_uniform4[4] = {
1./4., 1./4.,1./4., 1./4.
};
static const float pd_uniform8[8] = {
1./8., 1./8.,1./8., 1./8.,1./8., 1./8.,1./8., 1./8.
};
static const float pd_uniform16[16] = {
1./16., 1./16., 1./16., 1./16.,1./16., 1./16.,1./16., 1./16.,
1./16., 1./16., 1./16., 1./16.,1./16., 1./16.,1./16., 1./16.
};
static const float pd_uniform32[32] = {
1./32., 1./32., 1./32., 1./32.,1./32., 1./32.,1./32., 1./32.,
1./32., 1./32., 1./32., 1./32.,1./32., 1./32.,1./32., 1./32.,
1./32., 1./32., 1./32., 1./32.,1./32., 1./32.,1./32., 1./32.,
1./32., 1./32., 1./32., 1./32.,1./32., 1./32.,1./32., 1./32.
};
static const float pd_uniform64[64] = {
1./64., 1./64., 1./64., 1./64.,1./64., 1./64.,1./64., 1./64.,
1./64., 1./64., 1./64., 1./64.,1./64., 1./64.,1./64., 1./64.,
1./64., 1./64., 1./64., 1./64.,1./64., 1./64.,1./64., 1./64.,
1./64., 1./64., 1./64., 1./64.,1./64., 1./64.,1./64., 1./64.,
1./64., 1./64., 1./64., 1./64.,1./64., 1./64.,1./64., 1./64.,
1./64., 1./64., 1./64., 1./64.,1./64., 1./64.,1./64., 1./64.,
1./64., 1./64., 1./64., 1./64.,1./64., 1./64.,1./64., 1./64.,
1./64., 1./64., 1./64., 1./64.,1./64., 1./64.,1./64., 1./64.
};
static const ppd_uniform pd_uniform_tab[7] = {
pd_uniform1,
pd_uniform2,
pd_uniform4,
pd_uniform8,
pd_uniform16,
pd_uniform32,
pd_uniform64
};
// returns a pointer to the uniform distribution of the given logsize
const float *pd_uniform(int nlogdim)
{
return pd_uniform_tab[nlogdim];
}
// in-place multiplication functions
// compute dst = dst*src for any element of the distrib
static void pd_imul1(float *dst, const float *src)
{
dst[0] *= src[0];
}
static void pd_imul2(float *dst, const float *src)
{
dst[0] *= src[0]; dst[1] *= src[1];
}
static void pd_imul4(float *dst, const float *src)
{
dst[0] *= src[0]; dst[1] *= src[1];
dst[2] *= src[2]; dst[3] *= src[3];
}
static void pd_imul8(float *dst, const float *src)
{
dst[0] *= src[0]; dst[1] *= src[1]; dst[2] *= src[2]; dst[3] *= src[3];
dst[4] *= src[4]; dst[5] *= src[5]; dst[6] *= src[6]; dst[7] *= src[7];
}
static void pd_imul16(float *dst, const float *src)
{
dst[0] *= src[0]; dst[1] *= src[1]; dst[2] *= src[2]; dst[3] *= src[3];
dst[4] *= src[4]; dst[5] *= src[5]; dst[6] *= src[6]; dst[7] *= src[7];
dst[8] *= src[8]; dst[9] *= src[9]; dst[10]*= src[10]; dst[11]*= src[11];
dst[12]*= src[12]; dst[13]*= src[13]; dst[14]*= src[14]; dst[15]*= src[15];
}
static void pd_imul32(float *dst, const float *src)
{
pd_imul16(dst,src);
pd_imul16(dst+16,src+16);
}
static void pd_imul64(float *dst, const float *src)
{
pd_imul16(dst, src);
pd_imul16(dst+16, src+16);
pd_imul16(dst+32, src+32);
pd_imul16(dst+48, src+48);
}
static const ppd_imul pd_imul_tab[7] = {
pd_imul1,
pd_imul2,
pd_imul4,
pd_imul8,
pd_imul16,
pd_imul32,
pd_imul64
};
// in place multiplication
// compute dst = dst*src for any element of the distrib give their log2 size
// arguments must be pointers to array of floats of the given size
void pd_imul(float *dst, const float *src, int nlogdim)
{
pd_imul_tab[nlogdim](dst,src);
}
static float pd_norm1(float *ppd)
{
float t = ppd[0];
ppd[0] = 1.f;
return t;
}
static float pd_norm2(float *ppd)
{
float t,to;
t =ppd[0]; t +=ppd[1];
if (t<=0) {
pd_init(ppd,pd_uniform(1),pd_log2dim[1]);
return t;
}
to = t;
t = 1.f/t;
ppd[0] *=t; ppd[1] *=t;
return to;
}
static float pd_norm4(float *ppd)
{
float t,to;
t =ppd[0]; t +=ppd[1]; t +=ppd[2]; t +=ppd[3];
if (t<=0) {
pd_init(ppd,pd_uniform(2),pd_log2dim[2]);
return t;
}
to = t;
t = 1.f/t;
ppd[0] *=t; ppd[1] *=t; ppd[2] *=t; ppd[3] *=t;
return to;
}
static float pd_norm8(float *ppd)
{
float t,to;
t =ppd[0]; t +=ppd[1]; t +=ppd[2]; t +=ppd[3];
t +=ppd[4]; t +=ppd[5]; t +=ppd[6]; t +=ppd[7];
if (t<=0) {
pd_init(ppd,pd_uniform(3),pd_log2dim[3]);
return t;
}
to = t;
t = 1.f/t;
ppd[0] *=t; ppd[1] *=t; ppd[2] *=t; ppd[3] *=t;
ppd[4] *=t; ppd[5] *=t; ppd[6] *=t; ppd[7] *=t;
return to;
}
static float pd_norm16(float *ppd)
{
float t,to;
t =ppd[0]; t +=ppd[1]; t +=ppd[2]; t +=ppd[3];
t +=ppd[4]; t +=ppd[5]; t +=ppd[6]; t +=ppd[7];
t +=ppd[8]; t +=ppd[9]; t +=ppd[10]; t +=ppd[11];
t +=ppd[12]; t +=ppd[13]; t +=ppd[14]; t +=ppd[15];
if (t<=0) {
pd_init(ppd,pd_uniform(4),pd_log2dim[4]);
return t;
}
to = t;
t = 1.f/t;
ppd[0] *=t; ppd[1] *=t; ppd[2] *=t; ppd[3] *=t;
ppd[4] *=t; ppd[5] *=t; ppd[6] *=t; ppd[7] *=t;
ppd[8] *=t; ppd[9] *=t; ppd[10] *=t; ppd[11] *=t;
ppd[12] *=t; ppd[13] *=t; ppd[14] *=t; ppd[15] *=t;
return to;
}
static float pd_norm32(float *ppd)
{
float t,to;
t =ppd[0]; t +=ppd[1]; t +=ppd[2]; t +=ppd[3];
t +=ppd[4]; t +=ppd[5]; t +=ppd[6]; t +=ppd[7];
t +=ppd[8]; t +=ppd[9]; t +=ppd[10]; t +=ppd[11];
t +=ppd[12]; t +=ppd[13]; t +=ppd[14]; t +=ppd[15];
t +=ppd[16]; t +=ppd[17]; t +=ppd[18]; t +=ppd[19];
t +=ppd[20]; t +=ppd[21]; t +=ppd[22]; t +=ppd[23];
t +=ppd[24]; t +=ppd[25]; t +=ppd[26]; t +=ppd[27];
t +=ppd[28]; t +=ppd[29]; t +=ppd[30]; t +=ppd[31];
if (t<=0) {
pd_init(ppd,pd_uniform(5),pd_log2dim[5]);
return t;
}
to = t;
t = 1.f/t;
ppd[0] *=t; ppd[1] *=t; ppd[2] *=t; ppd[3] *=t;
ppd[4] *=t; ppd[5] *=t; ppd[6] *=t; ppd[7] *=t;
ppd[8] *=t; ppd[9] *=t; ppd[10] *=t; ppd[11] *=t;
ppd[12] *=t; ppd[13] *=t; ppd[14] *=t; ppd[15] *=t;
ppd[16] *=t; ppd[17] *=t; ppd[18] *=t; ppd[19] *=t;
ppd[20] *=t; ppd[21] *=t; ppd[22] *=t; ppd[23] *=t;
ppd[24] *=t; ppd[25] *=t; ppd[26] *=t; ppd[27] *=t;
ppd[28] *=t; ppd[29] *=t; ppd[30] *=t; ppd[31] *=t;
return to;
}
static float pd_norm64(float *ppd)
{
float t,to;
t =ppd[0]; t +=ppd[1]; t +=ppd[2]; t +=ppd[3];
t +=ppd[4]; t +=ppd[5]; t +=ppd[6]; t +=ppd[7];
t +=ppd[8]; t +=ppd[9]; t +=ppd[10]; t +=ppd[11];
t +=ppd[12]; t +=ppd[13]; t +=ppd[14]; t +=ppd[15];
t +=ppd[16]; t +=ppd[17]; t +=ppd[18]; t +=ppd[19];
t +=ppd[20]; t +=ppd[21]; t +=ppd[22]; t +=ppd[23];
t +=ppd[24]; t +=ppd[25]; t +=ppd[26]; t +=ppd[27];
t +=ppd[28]; t +=ppd[29]; t +=ppd[30]; t +=ppd[31];
t +=ppd[32]; t +=ppd[33]; t +=ppd[34]; t +=ppd[35];
t +=ppd[36]; t +=ppd[37]; t +=ppd[38]; t +=ppd[39];
t +=ppd[40]; t +=ppd[41]; t +=ppd[42]; t +=ppd[43];
t +=ppd[44]; t +=ppd[45]; t +=ppd[46]; t +=ppd[47];
t +=ppd[48]; t +=ppd[49]; t +=ppd[50]; t +=ppd[51];
t +=ppd[52]; t +=ppd[53]; t +=ppd[54]; t +=ppd[55];
t +=ppd[56]; t +=ppd[57]; t +=ppd[58]; t +=ppd[59];
t +=ppd[60]; t +=ppd[61]; t +=ppd[62]; t +=ppd[63];
if (t<=0) {
pd_init(ppd,pd_uniform(6),pd_log2dim[6]);
return t;
}
to = t;
t = 1.0f/t;
ppd[0] *=t; ppd[1] *=t; ppd[2] *=t; ppd[3] *=t;
ppd[4] *=t; ppd[5] *=t; ppd[6] *=t; ppd[7] *=t;
ppd[8] *=t; ppd[9] *=t; ppd[10] *=t; ppd[11] *=t;
ppd[12] *=t; ppd[13] *=t; ppd[14] *=t; ppd[15] *=t;
ppd[16] *=t; ppd[17] *=t; ppd[18] *=t; ppd[19] *=t;
ppd[20] *=t; ppd[21] *=t; ppd[22] *=t; ppd[23] *=t;
ppd[24] *=t; ppd[25] *=t; ppd[26] *=t; ppd[27] *=t;
ppd[28] *=t; ppd[29] *=t; ppd[30] *=t; ppd[31] *=t;
ppd[32] *=t; ppd[33] *=t; ppd[34] *=t; ppd[35] *=t;
ppd[36] *=t; ppd[37] *=t; ppd[38] *=t; ppd[39] *=t;
ppd[40] *=t; ppd[41] *=t; ppd[42] *=t; ppd[43] *=t;
ppd[44] *=t; ppd[45] *=t; ppd[46] *=t; ppd[47] *=t;
ppd[48] *=t; ppd[49] *=t; ppd[50] *=t; ppd[51] *=t;
ppd[52] *=t; ppd[53] *=t; ppd[54] *=t; ppd[55] *=t;
ppd[56] *=t; ppd[57] *=t; ppd[58] *=t; ppd[59] *=t;
ppd[60] *=t; ppd[61] *=t; ppd[62] *=t; ppd[63] *=t;
return to;
}
static const ppd_norm pd_norm_tab[7] = {
pd_norm1,
pd_norm2,
pd_norm4,
pd_norm8,
pd_norm16,
pd_norm32,
pd_norm64
};
float pd_norm(float *pd, int nlogdim)
{
return pd_norm_tab[nlogdim](pd);
}
void pd_memset(float *dst, const float *src, int ndim, int nitems)
{
int size = PD_SIZE(ndim);
while(nitems--) {
memcpy(dst,src,size);
dst +=ndim;
}
}
void pd_fwdperm(float *dst, float *src, const int *perm, int ndim)
{
// TODO: non-loop implementation
while (ndim--)
dst[ndim] = src[perm[ndim]];
}
void pd_bwdperm(float *dst, float *src, const int *perm, int ndim)
{
// TODO: non-loop implementation
while (ndim--)
dst[perm[ndim]] = src[ndim];
}
float pd_max(float *src, int ndim)
{
// TODO: faster implementation
float cmax=0; // we assume that prob distributions are always positive
float cval;
while (ndim--) {
cval = src[ndim];
if (cval>=cmax) {
cmax = cval;
}
}
return cmax;
}
int pd_argmax(float *pmax, float *src, int ndim)
{
// TODO: faster implementation
float cmax=0; // we assume that prob distributions are always positive
float cval;
int idxmax=-1; // indicates that all pd elements are <0
while (ndim--) {
cval = src[ndim];
if (cval>=cmax) {
cmax = cval;
idxmax = ndim;
}
}
if (pmax)
*pmax = cmax;
return idxmax;
}

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// pdmath.h
// Elementary math on probability distributions
//
// (c) 2016 - Nico Palermo, IV3NWV - Microtelecom Srl, Italy
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (repeat and accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#ifndef _pdmath_h_
#define _pdmath_h_
#include <memory.h>
#ifdef __cplusplus
extern "C" {
#endif
#define PD_NDIM(nlogdim) ((1<<(nlogdim))
#define PD_SIZE(ndim) ((ndim)*sizeof(float))
#define PD_ROWADDR(fp,ndim,idx) (fp+((ndim)*(idx)))
const float *pd_uniform(int nlogdim);
// Returns a pointer to a (constant) uniform distribution of the given log2 size
#define pd_init(dst,src,ndim) memcpy(dst,src,PD_SIZE(ndim))
// Distribution copy
void pd_memset(float *dst, const float *src, int ndim, int nitems);
// Copy the distribution pointed by src to the array of distributions dst
// src is a pointer to the input distribution (a vector of size ndim)
// dst is a pointer to a linear array of distributions (a vector of size ndim*nitems)
void pd_imul(float *dst, const float *src, int nlogdim);
// In place multiplication
// Compute dst = dst*src for any element of the distrib give their log2 size
// src and dst arguments must be pointers to array of floats of the given size
float pd_norm(float *pd, int nlogdim);
// In place normalizazion
// Normalizes the input vector so that the sum of its components are one
// pd must be a pointer to an array of floats of the given size.
// If the norm of the input vector is non-positive the vector components
// are replaced with a uniform distribution
// Returns the norm of the distribution prior to the normalization
void pd_fwdperm(float *dst, float *src, const int *perm, int ndim);
// Forward permutation of a distribution
// Computes dst[k] = src[perm[k]] for every element in the distribution
// perm must be a pointer to an array of integers of length ndim
void pd_bwdperm(float *dst, float *src, const int *perm, int ndim);
// Backward permutation of a distribution
// Computes dst[perm[k]] = src[k] for every element in the distribution
// perm must be a pointer to an array of integers of length ndim
float pd_max(float *src, int ndim);
// Return the maximum of the elements of the given distribution
// Assumes that the input vector is a probability distribution and that each element in the
// distribution is non negative
int pd_argmax(float *pmax, float *src, int ndim);
// Return the index of the maximum element of the given distribution
// The maximum is stored in the variable pointed by pmax if pmax is not null
// Same note of pd_max applies.
// Return -1 if all the elements in the distribution are negative
#ifdef __cplusplus
}
#endif
#endif // _pdmath_h_

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// qra12_63_64_irr_b.c
// Encoding/Decoding tables for Q-ary RA code (12,63) over GF(64)
// Code Name: qra12_63_64_irr_b
// (12,63) RA Code over GF(64) - RF=333344455567
// (c) 2016 - Nico Palermo - IV3NWV - Microtelecom Srl, Italy
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#include "qra12_63_64_irr_b.h"
#define qra_K 12 // number of information symbols
#define qra_N 63 // codeword length in symbols
#define qra_m 6 // bits/symbol
#define qra_M 64 // Symbol alphabet cardinality
#define qra_a 1 // grouping factor
#define qra_NC 51 // number of check symbols (N-K)
// Defines used by the message passing decoder --------
#define qra_V 63 // number of variables in the code graph (N)
#define qra_C 115 // number of factors in the code graph (N +(N-K)+1)
#define qra_NMSG 217 // number of msgs in the code graph
#define qra_MAXVDEG 8 // maximum variable degree
#define qra_MAXCDEG 3 // maximum factor degree
#define qra_R 0.19048f // code rate (K/N)
#define CODE_NAME "qra_12_63_64_irr_b"
// table of the systematic symbols indexes in the accumulator chain
static const int qra_acc_input_idx[qra_NC+1] = {
3, 11, 0, 1, 7, 8, 6, 5, 10, 4,
11, 9, 0, 2, 6, 7, 8, 4, 11, 5,
10, 2, 1, 9, 3, 8, 4, 11, 5, 7,
10, 9, 6, 3, 11, 5, 8, 10, 0, 7,
9, 11, 4, 2, 10, 6, 8, 1, 9, 7,
11, 10
};
// table of the systematic symbols weight logarithms over GF(M)
static const int qra_acc_input_wlog[qra_NC+1] = {
39, 0, 34, 16, 25, 0, 34, 48, 19, 13,
29, 56, 0, 5, 39, 42, 31, 0, 10, 0,
57, 62, 33, 43, 0, 14, 22, 48, 28, 20,
5, 45, 16, 43, 17, 4, 32, 0, 31, 0,
0, 28, 57, 0, 18, 0, 60, 0, 10, 31,
57, 27
};
// table of the logarithms of the elements of GF(M) (log(0) never used)
static const int qra_log[qra_M] = {
-1, 0, 1, 6, 2, 12, 7, 26, 3, 32,
13, 35, 8, 48, 27, 18, 4, 24, 33, 16,
14, 52, 36, 54, 9, 45, 49, 38, 28, 41,
19, 56, 5, 62, 25, 11, 34, 31, 17, 47,
15, 23, 53, 51, 37, 44, 55, 40, 10, 61,
46, 30, 50, 22, 39, 43, 29, 60, 42, 21,
20, 59, 57, 58
};
// table of GF(M) elements given their logarithm
static const int qra_exp[qra_M-1] = {
1, 2, 4, 8, 16, 32, 3, 6, 12, 24,
48, 35, 5, 10, 20, 40, 19, 38, 15, 30,
60, 59, 53, 41, 17, 34, 7, 14, 28, 56,
51, 37, 9, 18, 36, 11, 22, 44, 27, 54,
47, 29, 58, 55, 45, 25, 50, 39, 13, 26,
52, 43, 21, 42, 23, 46, 31, 62, 63, 61,
57, 49, 33
};
// table of the messages weight logarithms over GF(M)
static const int qra_msgw[qra_NMSG] = {
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 39, 0, 34, 16, 25, 0, 34,
48, 19, 13, 29, 56, 0, 5, 39, 42, 31,
0, 10, 0, 57, 62, 33, 43, 0, 14, 22,
48, 28, 20, 5, 45, 16, 43, 17, 4, 32,
0, 31, 0, 0, 28, 57, 0, 18, 0, 60,
0, 10, 31, 57, 27, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0
};
// table of the degrees of the variable nodes
static const int qra_vdeg[qra_V] = {
4, 4, 4, 4, 5, 5, 5, 6, 6, 6,
7, 8, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3
};
// table of the degrees of the factor nodes
static const int qra_cdeg[qra_C] = {
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 2, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 2
};
// table (uncompressed) of the v->c message indexes (-1=unused entry)
static const int qra_v2cmidx[qra_V*qra_MAXVDEG] = {
0, 65, 75, 101, -1, -1, -1, -1,
1, 66, 85, 110, -1, -1, -1, -1,
2, 76, 84, 106, -1, -1, -1, -1,
3, 63, 87, 96, -1, -1, -1, -1,
4, 72, 80, 89, 105, -1, -1, -1,
5, 70, 82, 91, 98, -1, -1, -1,
6, 69, 77, 95, 108, -1, -1, -1,
7, 67, 78, 92, 102, 112, -1, -1,
8, 68, 79, 88, 99, 109, -1, -1,
9, 74, 86, 94, 103, 111, -1, -1,
10, 71, 83, 93, 100, 107, 114, -1,
11, 64, 73, 81, 90, 97, 104, 113,
12, 115, 116, -1, -1, -1, -1, -1,
13, 117, 118, -1, -1, -1, -1, -1,
14, 119, 120, -1, -1, -1, -1, -1,
15, 121, 122, -1, -1, -1, -1, -1,
16, 123, 124, -1, -1, -1, -1, -1,
17, 125, 126, -1, -1, -1, -1, -1,
18, 127, 128, -1, -1, -1, -1, -1,
19, 129, 130, -1, -1, -1, -1, -1,
20, 131, 132, -1, -1, -1, -1, -1,
21, 133, 134, -1, -1, -1, -1, -1,
22, 135, 136, -1, -1, -1, -1, -1,
23, 137, 138, -1, -1, -1, -1, -1,
24, 139, 140, -1, -1, -1, -1, -1,
25, 141, 142, -1, -1, -1, -1, -1,
26, 143, 144, -1, -1, -1, -1, -1,
27, 145, 146, -1, -1, -1, -1, -1,
28, 147, 148, -1, -1, -1, -1, -1,
29, 149, 150, -1, -1, -1, -1, -1,
30, 151, 152, -1, -1, -1, -1, -1,
31, 153, 154, -1, -1, -1, -1, -1,
32, 155, 156, -1, -1, -1, -1, -1,
33, 157, 158, -1, -1, -1, -1, -1,
34, 159, 160, -1, -1, -1, -1, -1,
35, 161, 162, -1, -1, -1, -1, -1,
36, 163, 164, -1, -1, -1, -1, -1,
37, 165, 166, -1, -1, -1, -1, -1,
38, 167, 168, -1, -1, -1, -1, -1,
39, 169, 170, -1, -1, -1, -1, -1,
40, 171, 172, -1, -1, -1, -1, -1,
41, 173, 174, -1, -1, -1, -1, -1,
42, 175, 176, -1, -1, -1, -1, -1,
43, 177, 178, -1, -1, -1, -1, -1,
44, 179, 180, -1, -1, -1, -1, -1,
45, 181, 182, -1, -1, -1, -1, -1,
46, 183, 184, -1, -1, -1, -1, -1,
47, 185, 186, -1, -1, -1, -1, -1,
48, 187, 188, -1, -1, -1, -1, -1,
49, 189, 190, -1, -1, -1, -1, -1,
50, 191, 192, -1, -1, -1, -1, -1,
51, 193, 194, -1, -1, -1, -1, -1,
52, 195, 196, -1, -1, -1, -1, -1,
53, 197, 198, -1, -1, -1, -1, -1,
54, 199, 200, -1, -1, -1, -1, -1,
55, 201, 202, -1, -1, -1, -1, -1,
56, 203, 204, -1, -1, -1, -1, -1,
57, 205, 206, -1, -1, -1, -1, -1,
58, 207, 208, -1, -1, -1, -1, -1,
59, 209, 210, -1, -1, -1, -1, -1,
60, 211, 212, -1, -1, -1, -1, -1,
61, 213, 214, -1, -1, -1, -1, -1,
62, 215, 216, -1, -1, -1, -1, -1
};
// table (uncompressed) of the c->v message indexes (-1=unused entry)
static const int qra_c2vmidx[qra_C*qra_MAXCDEG] = {
0, -1, -1, 1, -1, -1, 2, -1, -1, 3, -1, -1,
4, -1, -1, 5, -1, -1, 6, -1, -1, 7, -1, -1,
8, -1, -1, 9, -1, -1, 10, -1, -1, 11, -1, -1,
12, -1, -1, 13, -1, -1, 14, -1, -1, 15, -1, -1,
16, -1, -1, 17, -1, -1, 18, -1, -1, 19, -1, -1,
20, -1, -1, 21, -1, -1, 22, -1, -1, 23, -1, -1,
24, -1, -1, 25, -1, -1, 26, -1, -1, 27, -1, -1,
28, -1, -1, 29, -1, -1, 30, -1, -1, 31, -1, -1,
32, -1, -1, 33, -1, -1, 34, -1, -1, 35, -1, -1,
36, -1, -1, 37, -1, -1, 38, -1, -1, 39, -1, -1,
40, -1, -1, 41, -1, -1, 42, -1, -1, 43, -1, -1,
44, -1, -1, 45, -1, -1, 46, -1, -1, 47, -1, -1,
48, -1, -1, 49, -1, -1, 50, -1, -1, 51, -1, -1,
52, -1, -1, 53, -1, -1, 54, -1, -1, 55, -1, -1,
56, -1, -1, 57, -1, -1, 58, -1, -1, 59, -1, -1,
60, -1, -1, 61, -1, -1, 62, -1, -1, 63, 115, -1,
64, 116, 117, 65, 118, 119, 66, 120, 121, 67, 122, 123,
68, 124, 125, 69, 126, 127, 70, 128, 129, 71, 130, 131,
72, 132, 133, 73, 134, 135, 74, 136, 137, 75, 138, 139,
76, 140, 141, 77, 142, 143, 78, 144, 145, 79, 146, 147,
80, 148, 149, 81, 150, 151, 82, 152, 153, 83, 154, 155,
84, 156, 157, 85, 158, 159, 86, 160, 161, 87, 162, 163,
88, 164, 165, 89, 166, 167, 90, 168, 169, 91, 170, 171,
92, 172, 173, 93, 174, 175, 94, 176, 177, 95, 178, 179,
96, 180, 181, 97, 182, 183, 98, 184, 185, 99, 186, 187,
100, 188, 189, 101, 190, 191, 102, 192, 193, 103, 194, 195,
104, 196, 197, 105, 198, 199, 106, 200, 201, 107, 202, 203,
108, 204, 205, 109, 206, 207, 110, 208, 209, 111, 210, 211,
112, 212, 213, 113, 214, 215, 114, 216, -1
};
// permutation matrix to compute Prob(x*alfa^logw)
static const int qra_pmat[qra_M*qra_M] = {
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,
0, 33, 1, 32, 2, 35, 3, 34, 4, 37, 5, 36, 6, 39, 7, 38,
8, 41, 9, 40, 10, 43, 11, 42, 12, 45, 13, 44, 14, 47, 15, 46,
16, 49, 17, 48, 18, 51, 19, 50, 20, 53, 21, 52, 22, 55, 23, 54,
24, 57, 25, 56, 26, 59, 27, 58, 28, 61, 29, 60, 30, 63, 31, 62,
0, 49, 33, 16, 1, 48, 32, 17, 2, 51, 35, 18, 3, 50, 34, 19,
4, 53, 37, 20, 5, 52, 36, 21, 6, 55, 39, 22, 7, 54, 38, 23,
8, 57, 41, 24, 9, 56, 40, 25, 10, 59, 43, 26, 11, 58, 42, 27,
12, 61, 45, 28, 13, 60, 44, 29, 14, 63, 47, 30, 15, 62, 46, 31,
0, 57, 49, 8, 33, 24, 16, 41, 1, 56, 48, 9, 32, 25, 17, 40,
2, 59, 51, 10, 35, 26, 18, 43, 3, 58, 50, 11, 34, 27, 19, 42,
4, 61, 53, 12, 37, 28, 20, 45, 5, 60, 52, 13, 36, 29, 21, 44,
6, 63, 55, 14, 39, 30, 22, 47, 7, 62, 54, 15, 38, 31, 23, 46,
0, 61, 57, 4, 49, 12, 8, 53, 33, 28, 24, 37, 16, 45, 41, 20,
1, 60, 56, 5, 48, 13, 9, 52, 32, 29, 25, 36, 17, 44, 40, 21,
2, 63, 59, 6, 51, 14, 10, 55, 35, 30, 26, 39, 18, 47, 43, 22,
3, 62, 58, 7, 50, 15, 11, 54, 34, 31, 27, 38, 19, 46, 42, 23,
0, 63, 61, 2, 57, 6, 4, 59, 49, 14, 12, 51, 8, 55, 53, 10,
33, 30, 28, 35, 24, 39, 37, 26, 16, 47, 45, 18, 41, 22, 20, 43,
1, 62, 60, 3, 56, 7, 5, 58, 48, 15, 13, 50, 9, 54, 52, 11,
32, 31, 29, 34, 25, 38, 36, 27, 17, 46, 44, 19, 40, 23, 21, 42,
0, 62, 63, 1, 61, 3, 2, 60, 57, 7, 6, 56, 4, 58, 59, 5,
49, 15, 14, 48, 12, 50, 51, 13, 8, 54, 55, 9, 53, 11, 10, 52,
33, 31, 30, 32, 28, 34, 35, 29, 24, 38, 39, 25, 37, 27, 26, 36,
16, 46, 47, 17, 45, 19, 18, 44, 41, 23, 22, 40, 20, 42, 43, 21,
0, 31, 62, 33, 63, 32, 1, 30, 61, 34, 3, 28, 2, 29, 60, 35,
57, 38, 7, 24, 6, 25, 56, 39, 4, 27, 58, 37, 59, 36, 5, 26,
49, 46, 15, 16, 14, 17, 48, 47, 12, 19, 50, 45, 51, 44, 13, 18,
8, 23, 54, 41, 55, 40, 9, 22, 53, 42, 11, 20, 10, 21, 52, 43,
0, 46, 31, 49, 62, 16, 33, 15, 63, 17, 32, 14, 1, 47, 30, 48,
61, 19, 34, 12, 3, 45, 28, 50, 2, 44, 29, 51, 60, 18, 35, 13,
57, 23, 38, 8, 7, 41, 24, 54, 6, 40, 25, 55, 56, 22, 39, 9,
4, 42, 27, 53, 58, 20, 37, 11, 59, 21, 36, 10, 5, 43, 26, 52,
0, 23, 46, 57, 31, 8, 49, 38, 62, 41, 16, 7, 33, 54, 15, 24,
63, 40, 17, 6, 32, 55, 14, 25, 1, 22, 47, 56, 30, 9, 48, 39,
61, 42, 19, 4, 34, 53, 12, 27, 3, 20, 45, 58, 28, 11, 50, 37,
2, 21, 44, 59, 29, 10, 51, 36, 60, 43, 18, 5, 35, 52, 13, 26,
0, 42, 23, 61, 46, 4, 57, 19, 31, 53, 8, 34, 49, 27, 38, 12,
62, 20, 41, 3, 16, 58, 7, 45, 33, 11, 54, 28, 15, 37, 24, 50,
63, 21, 40, 2, 17, 59, 6, 44, 32, 10, 55, 29, 14, 36, 25, 51,
1, 43, 22, 60, 47, 5, 56, 18, 30, 52, 9, 35, 48, 26, 39, 13,
0, 21, 42, 63, 23, 2, 61, 40, 46, 59, 4, 17, 57, 44, 19, 6,
31, 10, 53, 32, 8, 29, 34, 55, 49, 36, 27, 14, 38, 51, 12, 25,
62, 43, 20, 1, 41, 60, 3, 22, 16, 5, 58, 47, 7, 18, 45, 56,
33, 52, 11, 30, 54, 35, 28, 9, 15, 26, 37, 48, 24, 13, 50, 39,
0, 43, 21, 62, 42, 1, 63, 20, 23, 60, 2, 41, 61, 22, 40, 3,
46, 5, 59, 16, 4, 47, 17, 58, 57, 18, 44, 7, 19, 56, 6, 45,
31, 52, 10, 33, 53, 30, 32, 11, 8, 35, 29, 54, 34, 9, 55, 28,
49, 26, 36, 15, 27, 48, 14, 37, 38, 13, 51, 24, 12, 39, 25, 50,
0, 52, 43, 31, 21, 33, 62, 10, 42, 30, 1, 53, 63, 11, 20, 32,
23, 35, 60, 8, 2, 54, 41, 29, 61, 9, 22, 34, 40, 28, 3, 55,
46, 26, 5, 49, 59, 15, 16, 36, 4, 48, 47, 27, 17, 37, 58, 14,
57, 13, 18, 38, 44, 24, 7, 51, 19, 39, 56, 12, 6, 50, 45, 25,
0, 26, 52, 46, 43, 49, 31, 5, 21, 15, 33, 59, 62, 36, 10, 16,
42, 48, 30, 4, 1, 27, 53, 47, 63, 37, 11, 17, 20, 14, 32, 58,
23, 13, 35, 57, 60, 38, 8, 18, 2, 24, 54, 44, 41, 51, 29, 7,
61, 39, 9, 19, 22, 12, 34, 56, 40, 50, 28, 6, 3, 25, 55, 45,
0, 13, 26, 23, 52, 57, 46, 35, 43, 38, 49, 60, 31, 18, 5, 8,
21, 24, 15, 2, 33, 44, 59, 54, 62, 51, 36, 41, 10, 7, 16, 29,
42, 39, 48, 61, 30, 19, 4, 9, 1, 12, 27, 22, 53, 56, 47, 34,
63, 50, 37, 40, 11, 6, 17, 28, 20, 25, 14, 3, 32, 45, 58, 55,
0, 39, 13, 42, 26, 61, 23, 48, 52, 19, 57, 30, 46, 9, 35, 4,
43, 12, 38, 1, 49, 22, 60, 27, 31, 56, 18, 53, 5, 34, 8, 47,
21, 50, 24, 63, 15, 40, 2, 37, 33, 6, 44, 11, 59, 28, 54, 17,
62, 25, 51, 20, 36, 3, 41, 14, 10, 45, 7, 32, 16, 55, 29, 58,
0, 50, 39, 21, 13, 63, 42, 24, 26, 40, 61, 15, 23, 37, 48, 2,
52, 6, 19, 33, 57, 11, 30, 44, 46, 28, 9, 59, 35, 17, 4, 54,
43, 25, 12, 62, 38, 20, 1, 51, 49, 3, 22, 36, 60, 14, 27, 41,
31, 45, 56, 10, 18, 32, 53, 7, 5, 55, 34, 16, 8, 58, 47, 29,
0, 25, 50, 43, 39, 62, 21, 12, 13, 20, 63, 38, 42, 51, 24, 1,
26, 3, 40, 49, 61, 36, 15, 22, 23, 14, 37, 60, 48, 41, 2, 27,
52, 45, 6, 31, 19, 10, 33, 56, 57, 32, 11, 18, 30, 7, 44, 53,
46, 55, 28, 5, 9, 16, 59, 34, 35, 58, 17, 8, 4, 29, 54, 47,
0, 45, 25, 52, 50, 31, 43, 6, 39, 10, 62, 19, 21, 56, 12, 33,
13, 32, 20, 57, 63, 18, 38, 11, 42, 7, 51, 30, 24, 53, 1, 44,
26, 55, 3, 46, 40, 5, 49, 28, 61, 16, 36, 9, 15, 34, 22, 59,
23, 58, 14, 35, 37, 8, 60, 17, 48, 29, 41, 4, 2, 47, 27, 54,
0, 55, 45, 26, 25, 46, 52, 3, 50, 5, 31, 40, 43, 28, 6, 49,
39, 16, 10, 61, 62, 9, 19, 36, 21, 34, 56, 15, 12, 59, 33, 22,
13, 58, 32, 23, 20, 35, 57, 14, 63, 8, 18, 37, 38, 17, 11, 60,
42, 29, 7, 48, 51, 4, 30, 41, 24, 47, 53, 2, 1, 54, 44, 27,
0, 58, 55, 13, 45, 23, 26, 32, 25, 35, 46, 20, 52, 14, 3, 57,
50, 8, 5, 63, 31, 37, 40, 18, 43, 17, 28, 38, 6, 60, 49, 11,
39, 29, 16, 42, 10, 48, 61, 7, 62, 4, 9, 51, 19, 41, 36, 30,
21, 47, 34, 24, 56, 2, 15, 53, 12, 54, 59, 1, 33, 27, 22, 44,
0, 29, 58, 39, 55, 42, 13, 16, 45, 48, 23, 10, 26, 7, 32, 61,
25, 4, 35, 62, 46, 51, 20, 9, 52, 41, 14, 19, 3, 30, 57, 36,
50, 47, 8, 21, 5, 24, 63, 34, 31, 2, 37, 56, 40, 53, 18, 15,
43, 54, 17, 12, 28, 1, 38, 59, 6, 27, 60, 33, 49, 44, 11, 22,
0, 47, 29, 50, 58, 21, 39, 8, 55, 24, 42, 5, 13, 34, 16, 63,
45, 2, 48, 31, 23, 56, 10, 37, 26, 53, 7, 40, 32, 15, 61, 18,
25, 54, 4, 43, 35, 12, 62, 17, 46, 1, 51, 28, 20, 59, 9, 38,
52, 27, 41, 6, 14, 33, 19, 60, 3, 44, 30, 49, 57, 22, 36, 11,
0, 54, 47, 25, 29, 43, 50, 4, 58, 12, 21, 35, 39, 17, 8, 62,
55, 1, 24, 46, 42, 28, 5, 51, 13, 59, 34, 20, 16, 38, 63, 9,
45, 27, 2, 52, 48, 6, 31, 41, 23, 33, 56, 14, 10, 60, 37, 19,
26, 44, 53, 3, 7, 49, 40, 30, 32, 22, 15, 57, 61, 11, 18, 36,
0, 27, 54, 45, 47, 52, 25, 2, 29, 6, 43, 48, 50, 41, 4, 31,
58, 33, 12, 23, 21, 14, 35, 56, 39, 60, 17, 10, 8, 19, 62, 37,
55, 44, 1, 26, 24, 3, 46, 53, 42, 49, 28, 7, 5, 30, 51, 40,
13, 22, 59, 32, 34, 57, 20, 15, 16, 11, 38, 61, 63, 36, 9, 18,
0, 44, 27, 55, 54, 26, 45, 1, 47, 3, 52, 24, 25, 53, 2, 46,
29, 49, 6, 42, 43, 7, 48, 28, 50, 30, 41, 5, 4, 40, 31, 51,
58, 22, 33, 13, 12, 32, 23, 59, 21, 57, 14, 34, 35, 15, 56, 20,
39, 11, 60, 16, 17, 61, 10, 38, 8, 36, 19, 63, 62, 18, 37, 9,
0, 22, 44, 58, 27, 13, 55, 33, 54, 32, 26, 12, 45, 59, 1, 23,
47, 57, 3, 21, 52, 34, 24, 14, 25, 15, 53, 35, 2, 20, 46, 56,
29, 11, 49, 39, 6, 16, 42, 60, 43, 61, 7, 17, 48, 38, 28, 10,
50, 36, 30, 8, 41, 63, 5, 19, 4, 18, 40, 62, 31, 9, 51, 37,
0, 11, 22, 29, 44, 39, 58, 49, 27, 16, 13, 6, 55, 60, 33, 42,
54, 61, 32, 43, 26, 17, 12, 7, 45, 38, 59, 48, 1, 10, 23, 28,
47, 36, 57, 50, 3, 8, 21, 30, 52, 63, 34, 41, 24, 19, 14, 5,
25, 18, 15, 4, 53, 62, 35, 40, 2, 9, 20, 31, 46, 37, 56, 51,
0, 36, 11, 47, 22, 50, 29, 57, 44, 8, 39, 3, 58, 30, 49, 21,
27, 63, 16, 52, 13, 41, 6, 34, 55, 19, 60, 24, 33, 5, 42, 14,
54, 18, 61, 25, 32, 4, 43, 15, 26, 62, 17, 53, 12, 40, 7, 35,
45, 9, 38, 2, 59, 31, 48, 20, 1, 37, 10, 46, 23, 51, 28, 56,
0, 18, 36, 54, 11, 25, 47, 61, 22, 4, 50, 32, 29, 15, 57, 43,
44, 62, 8, 26, 39, 53, 3, 17, 58, 40, 30, 12, 49, 35, 21, 7,
27, 9, 63, 45, 16, 2, 52, 38, 13, 31, 41, 59, 6, 20, 34, 48,
55, 37, 19, 1, 60, 46, 24, 10, 33, 51, 5, 23, 42, 56, 14, 28,
0, 9, 18, 27, 36, 45, 54, 63, 11, 2, 25, 16, 47, 38, 61, 52,
22, 31, 4, 13, 50, 59, 32, 41, 29, 20, 15, 6, 57, 48, 43, 34,
44, 37, 62, 55, 8, 1, 26, 19, 39, 46, 53, 60, 3, 10, 17, 24,
58, 51, 40, 33, 30, 23, 12, 5, 49, 56, 35, 42, 21, 28, 7, 14,
0, 37, 9, 44, 18, 55, 27, 62, 36, 1, 45, 8, 54, 19, 63, 26,
11, 46, 2, 39, 25, 60, 16, 53, 47, 10, 38, 3, 61, 24, 52, 17,
22, 51, 31, 58, 4, 33, 13, 40, 50, 23, 59, 30, 32, 5, 41, 12,
29, 56, 20, 49, 15, 42, 6, 35, 57, 28, 48, 21, 43, 14, 34, 7,
0, 51, 37, 22, 9, 58, 44, 31, 18, 33, 55, 4, 27, 40, 62, 13,
36, 23, 1, 50, 45, 30, 8, 59, 54, 5, 19, 32, 63, 12, 26, 41,
11, 56, 46, 29, 2, 49, 39, 20, 25, 42, 60, 15, 16, 35, 53, 6,
47, 28, 10, 57, 38, 21, 3, 48, 61, 14, 24, 43, 52, 7, 17, 34,
0, 56, 51, 11, 37, 29, 22, 46, 9, 49, 58, 2, 44, 20, 31, 39,
18, 42, 33, 25, 55, 15, 4, 60, 27, 35, 40, 16, 62, 6, 13, 53,
36, 28, 23, 47, 1, 57, 50, 10, 45, 21, 30, 38, 8, 48, 59, 3,
54, 14, 5, 61, 19, 43, 32, 24, 63, 7, 12, 52, 26, 34, 41, 17,
0, 28, 56, 36, 51, 47, 11, 23, 37, 57, 29, 1, 22, 10, 46, 50,
9, 21, 49, 45, 58, 38, 2, 30, 44, 48, 20, 8, 31, 3, 39, 59,
18, 14, 42, 54, 33, 61, 25, 5, 55, 43, 15, 19, 4, 24, 60, 32,
27, 7, 35, 63, 40, 52, 16, 12, 62, 34, 6, 26, 13, 17, 53, 41,
0, 14, 28, 18, 56, 54, 36, 42, 51, 61, 47, 33, 11, 5, 23, 25,
37, 43, 57, 55, 29, 19, 1, 15, 22, 24, 10, 4, 46, 32, 50, 60,
9, 7, 21, 27, 49, 63, 45, 35, 58, 52, 38, 40, 2, 12, 30, 16,
44, 34, 48, 62, 20, 26, 8, 6, 31, 17, 3, 13, 39, 41, 59, 53,
0, 7, 14, 9, 28, 27, 18, 21, 56, 63, 54, 49, 36, 35, 42, 45,
51, 52, 61, 58, 47, 40, 33, 38, 11, 12, 5, 2, 23, 16, 25, 30,
37, 34, 43, 44, 57, 62, 55, 48, 29, 26, 19, 20, 1, 6, 15, 8,
22, 17, 24, 31, 10, 13, 4, 3, 46, 41, 32, 39, 50, 53, 60, 59,
0, 34, 7, 37, 14, 44, 9, 43, 28, 62, 27, 57, 18, 48, 21, 55,
56, 26, 63, 29, 54, 20, 49, 19, 36, 6, 35, 1, 42, 8, 45, 15,
51, 17, 52, 22, 61, 31, 58, 24, 47, 13, 40, 10, 33, 3, 38, 4,
11, 41, 12, 46, 5, 39, 2, 32, 23, 53, 16, 50, 25, 59, 30, 60,
0, 17, 34, 51, 7, 22, 37, 52, 14, 31, 44, 61, 9, 24, 43, 58,
28, 13, 62, 47, 27, 10, 57, 40, 18, 3, 48, 33, 21, 4, 55, 38,
56, 41, 26, 11, 63, 46, 29, 12, 54, 39, 20, 5, 49, 32, 19, 2,
36, 53, 6, 23, 35, 50, 1, 16, 42, 59, 8, 25, 45, 60, 15, 30,
0, 41, 17, 56, 34, 11, 51, 26, 7, 46, 22, 63, 37, 12, 52, 29,
14, 39, 31, 54, 44, 5, 61, 20, 9, 32, 24, 49, 43, 2, 58, 19,
28, 53, 13, 36, 62, 23, 47, 6, 27, 50, 10, 35, 57, 16, 40, 1,
18, 59, 3, 42, 48, 25, 33, 8, 21, 60, 4, 45, 55, 30, 38, 15,
0, 53, 41, 28, 17, 36, 56, 13, 34, 23, 11, 62, 51, 6, 26, 47,
7, 50, 46, 27, 22, 35, 63, 10, 37, 16, 12, 57, 52, 1, 29, 40,
14, 59, 39, 18, 31, 42, 54, 3, 44, 25, 5, 48, 61, 8, 20, 33,
9, 60, 32, 21, 24, 45, 49, 4, 43, 30, 2, 55, 58, 15, 19, 38,
0, 59, 53, 14, 41, 18, 28, 39, 17, 42, 36, 31, 56, 3, 13, 54,
34, 25, 23, 44, 11, 48, 62, 5, 51, 8, 6, 61, 26, 33, 47, 20,
7, 60, 50, 9, 46, 21, 27, 32, 22, 45, 35, 24, 63, 4, 10, 49,
37, 30, 16, 43, 12, 55, 57, 2, 52, 15, 1, 58, 29, 38, 40, 19,
0, 60, 59, 7, 53, 9, 14, 50, 41, 21, 18, 46, 28, 32, 39, 27,
17, 45, 42, 22, 36, 24, 31, 35, 56, 4, 3, 63, 13, 49, 54, 10,
34, 30, 25, 37, 23, 43, 44, 16, 11, 55, 48, 12, 62, 2, 5, 57,
51, 15, 8, 52, 6, 58, 61, 1, 26, 38, 33, 29, 47, 19, 20, 40,
0, 30, 60, 34, 59, 37, 7, 25, 53, 43, 9, 23, 14, 16, 50, 44,
41, 55, 21, 11, 18, 12, 46, 48, 28, 2, 32, 62, 39, 57, 27, 5,
17, 15, 45, 51, 42, 52, 22, 8, 36, 58, 24, 6, 31, 1, 35, 61,
56, 38, 4, 26, 3, 29, 63, 33, 13, 19, 49, 47, 54, 40, 10, 20,
0, 15, 30, 17, 60, 51, 34, 45, 59, 52, 37, 42, 7, 8, 25, 22,
53, 58, 43, 36, 9, 6, 23, 24, 14, 1, 16, 31, 50, 61, 44, 35,
41, 38, 55, 56, 21, 26, 11, 4, 18, 29, 12, 3, 46, 33, 48, 63,
28, 19, 2, 13, 32, 47, 62, 49, 39, 40, 57, 54, 27, 20, 5, 10,
0, 38, 15, 41, 30, 56, 17, 55, 60, 26, 51, 21, 34, 4, 45, 11,
59, 29, 52, 18, 37, 3, 42, 12, 7, 33, 8, 46, 25, 63, 22, 48,
53, 19, 58, 28, 43, 13, 36, 2, 9, 47, 6, 32, 23, 49, 24, 62,
14, 40, 1, 39, 16, 54, 31, 57, 50, 20, 61, 27, 44, 10, 35, 5,
0, 19, 38, 53, 15, 28, 41, 58, 30, 13, 56, 43, 17, 2, 55, 36,
60, 47, 26, 9, 51, 32, 21, 6, 34, 49, 4, 23, 45, 62, 11, 24,
59, 40, 29, 14, 52, 39, 18, 1, 37, 54, 3, 16, 42, 57, 12, 31,
7, 20, 33, 50, 8, 27, 46, 61, 25, 10, 63, 44, 22, 5, 48, 35,
0, 40, 19, 59, 38, 14, 53, 29, 15, 39, 28, 52, 41, 1, 58, 18,
30, 54, 13, 37, 56, 16, 43, 3, 17, 57, 2, 42, 55, 31, 36, 12,
60, 20, 47, 7, 26, 50, 9, 33, 51, 27, 32, 8, 21, 61, 6, 46,
34, 10, 49, 25, 4, 44, 23, 63, 45, 5, 62, 22, 11, 35, 24, 48,
0, 20, 40, 60, 19, 7, 59, 47, 38, 50, 14, 26, 53, 33, 29, 9,
15, 27, 39, 51, 28, 8, 52, 32, 41, 61, 1, 21, 58, 46, 18, 6,
30, 10, 54, 34, 13, 25, 37, 49, 56, 44, 16, 4, 43, 63, 3, 23,
17, 5, 57, 45, 2, 22, 42, 62, 55, 35, 31, 11, 36, 48, 12, 24,
0, 10, 20, 30, 40, 34, 60, 54, 19, 25, 7, 13, 59, 49, 47, 37,
38, 44, 50, 56, 14, 4, 26, 16, 53, 63, 33, 43, 29, 23, 9, 3,
15, 5, 27, 17, 39, 45, 51, 57, 28, 22, 8, 2, 52, 62, 32, 42,
41, 35, 61, 55, 1, 11, 21, 31, 58, 48, 46, 36, 18, 24, 6, 12,
0, 5, 10, 15, 20, 17, 30, 27, 40, 45, 34, 39, 60, 57, 54, 51,
19, 22, 25, 28, 7, 2, 13, 8, 59, 62, 49, 52, 47, 42, 37, 32,
38, 35, 44, 41, 50, 55, 56, 61, 14, 11, 4, 1, 26, 31, 16, 21,
53, 48, 63, 58, 33, 36, 43, 46, 29, 24, 23, 18, 9, 12, 3, 6,
0, 35, 5, 38, 10, 41, 15, 44, 20, 55, 17, 50, 30, 61, 27, 56,
40, 11, 45, 14, 34, 1, 39, 4, 60, 31, 57, 26, 54, 21, 51, 16,
19, 48, 22, 53, 25, 58, 28, 63, 7, 36, 2, 33, 13, 46, 8, 43,
59, 24, 62, 29, 49, 18, 52, 23, 47, 12, 42, 9, 37, 6, 32, 3,
0, 48, 35, 19, 5, 53, 38, 22, 10, 58, 41, 25, 15, 63, 44, 28,
20, 36, 55, 7, 17, 33, 50, 2, 30, 46, 61, 13, 27, 43, 56, 8,
40, 24, 11, 59, 45, 29, 14, 62, 34, 18, 1, 49, 39, 23, 4, 52,
60, 12, 31, 47, 57, 9, 26, 42, 54, 6, 21, 37, 51, 3, 16, 32,
0, 24, 48, 40, 35, 59, 19, 11, 5, 29, 53, 45, 38, 62, 22, 14,
10, 18, 58, 34, 41, 49, 25, 1, 15, 23, 63, 39, 44, 52, 28, 4,
20, 12, 36, 60, 55, 47, 7, 31, 17, 9, 33, 57, 50, 42, 2, 26,
30, 6, 46, 54, 61, 37, 13, 21, 27, 3, 43, 51, 56, 32, 8, 16,
0, 12, 24, 20, 48, 60, 40, 36, 35, 47, 59, 55, 19, 31, 11, 7,
5, 9, 29, 17, 53, 57, 45, 33, 38, 42, 62, 50, 22, 26, 14, 2,
10, 6, 18, 30, 58, 54, 34, 46, 41, 37, 49, 61, 25, 21, 1, 13,
15, 3, 23, 27, 63, 51, 39, 43, 44, 32, 52, 56, 28, 16, 4, 8,
0, 6, 12, 10, 24, 30, 20, 18, 48, 54, 60, 58, 40, 46, 36, 34,
35, 37, 47, 41, 59, 61, 55, 49, 19, 21, 31, 25, 11, 13, 7, 1,
5, 3, 9, 15, 29, 27, 17, 23, 53, 51, 57, 63, 45, 43, 33, 39,
38, 32, 42, 44, 62, 56, 50, 52, 22, 16, 26, 28, 14, 8, 2, 4,
0, 3, 6, 5, 12, 15, 10, 9, 24, 27, 30, 29, 20, 23, 18, 17,
48, 51, 54, 53, 60, 63, 58, 57, 40, 43, 46, 45, 36, 39, 34, 33,
35, 32, 37, 38, 47, 44, 41, 42, 59, 56, 61, 62, 55, 52, 49, 50,
19, 16, 21, 22, 31, 28, 25, 26, 11, 8, 13, 14, 7, 4, 1, 2,
0, 32, 3, 35, 6, 38, 5, 37, 12, 44, 15, 47, 10, 42, 9, 41,
24, 56, 27, 59, 30, 62, 29, 61, 20, 52, 23, 55, 18, 50, 17, 49,
48, 16, 51, 19, 54, 22, 53, 21, 60, 28, 63, 31, 58, 26, 57, 25,
40, 8, 43, 11, 46, 14, 45, 13, 36, 4, 39, 7, 34, 2, 33, 1,
0, 16, 32, 48, 3, 19, 35, 51, 6, 22, 38, 54, 5, 21, 37, 53,
12, 28, 44, 60, 15, 31, 47, 63, 10, 26, 42, 58, 9, 25, 41, 57,
24, 8, 56, 40, 27, 11, 59, 43, 30, 14, 62, 46, 29, 13, 61, 45,
20, 4, 52, 36, 23, 7, 55, 39, 18, 2, 50, 34, 17, 1, 49, 33,
0, 8, 16, 24, 32, 40, 48, 56, 3, 11, 19, 27, 35, 43, 51, 59,
6, 14, 22, 30, 38, 46, 54, 62, 5, 13, 21, 29, 37, 45, 53, 61,
12, 4, 28, 20, 44, 36, 60, 52, 15, 7, 31, 23, 47, 39, 63, 55,
10, 2, 26, 18, 42, 34, 58, 50, 9, 1, 25, 17, 41, 33, 57, 49,
0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60,
3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63,
6, 2, 14, 10, 22, 18, 30, 26, 38, 34, 46, 42, 54, 50, 62, 58,
5, 1, 13, 9, 21, 17, 29, 25, 37, 33, 45, 41, 53, 49, 61, 57,
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30,
32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62,
3, 1, 7, 5, 11, 9, 15, 13, 19, 17, 23, 21, 27, 25, 31, 29,
35, 33, 39, 37, 43, 41, 47, 45, 51, 49, 55, 53, 59, 57, 63, 61
};
const qracode qra_12_63_64_irr_b = {
qra_K,
qra_N,
qra_m,
qra_M,
qra_a,
qra_NC,
qra_V,
qra_C,
qra_NMSG,
qra_MAXVDEG,
qra_MAXCDEG,
QRATYPE_NORMAL,
qra_R,
CODE_NAME,
qra_acc_input_idx,
qra_acc_input_wlog,
qra_log,
qra_exp,
qra_msgw,
qra_vdeg,
qra_cdeg,
qra_v2cmidx,
qra_c2vmidx,
qra_pmat
};
#undef qra_K
#undef qra_N
#undef qra_m
#undef qra_M
#undef qra_a
#undef qra_NC
#undef qra_V
#undef qra_C
#undef qra_NMSG
#undef qra_MAXVDEG
#undef qra_MAXCDEG
#undef qra_R
#undef CODE_NAME

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// qra12_63_64_irr_b.h
// Code tables and defines for Q-ary RA code (12,63) over GF(64)
// Code Name: qra12_63_64_irr_b
// (12,63) RA Code over GF(64) - RF=333344455567
// (c) 2016 - Nico Palermo - IV3NWV - Microtelecom Srl, Italy
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#ifndef _qra12_63_64_irr_b_h
#define _qra12_63_64_irr_b_h
#include "qracodes.h"
#ifdef __cplusplus
extern "C" {
#endif
extern const qracode qra_12_63_64_irr_b;
#ifdef __cplusplus
}
#endif
#endif // _qra12_63_64_irr_b_h

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// qra13_64_64_irr_e.c
// Encoding/Decoding tables for Q-ary RA code (13,64) over GF(64)
// Code Name: qra13_64_64_irr_e
// (13,64) RA Code over GF(64) RF=[3x4 4x4 6x1 3x2 5x1 7x1]/18
// (c) 2016 - Nico Palermo - IV3NWV - Microtelecom Srl, Italy
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#include "qra13_64_64_irr_e.h"
#define qra_K 13 // number of information symbols
#define qra_N 64 // codeword length in symbols
#define qra_m 6 // bits/symbol
#define qra_M 64 // Symbol alphabet cardinality
#define qra_a 1 // grouping factor
#define qra_NC 51 // number of check symbols (N-K)
// Defines used by the message passing decoder --------
#define qra_V 64 // number of variables in the code graph (N)
#define qra_C 116 // number of factors in the code graph (N +(N-K)+1)
#define qra_NMSG 218 // number of msgs in the code graph
#define qra_MAXVDEG 8 // maximum variable degree
#define qra_MAXCDEG 3 // maximum factor degree
#define qra_R 0.20313f // code rate (K/N)
#define CODE_NAME "qra_13_64_64_irr_e"
// table of the systematic symbols indexes in the accumulator chain
static const int qra_acc_input_idx[qra_NC+1] = {
12, 4, 3, 9, 0, 11, 6, 8, 12, 1,
2, 7, 4, 11, 3, 5, 9, 8, 12, 7,
2, 4, 10, 3, 5, 11, 12, 8, 9, 6,
7, 2, 5, 4, 12, 8, 11, 1, 6, 7,
0, 10, 12, 8, 11, 5, 6, 1, 0, 10,
12, 8
};
// table of the systematic symbols weight logarithms over GF(M)
static const int qra_acc_input_wlog[qra_NC+1] = {
0, 27, 0, 0, 0, 31, 28, 61, 31, 0,
0, 52, 22, 7, 19, 47, 44, 62, 32, 50,
52, 42, 48, 56, 40, 50, 51, 37, 37, 0,
5, 14, 0, 0, 18, 2, 0, 45, 21, 0,
62, 8, 11, 60, 36, 32, 17, 9, 5, 0,
53, 0
};
// table of the logarithms of the elements of GF(M) (log(0) never used)
static const int qra_log[qra_M] = {
-1, 0, 1, 6, 2, 12, 7, 26, 3, 32,
13, 35, 8, 48, 27, 18, 4, 24, 33, 16,
14, 52, 36, 54, 9, 45, 49, 38, 28, 41,
19, 56, 5, 62, 25, 11, 34, 31, 17, 47,
15, 23, 53, 51, 37, 44, 55, 40, 10, 61,
46, 30, 50, 22, 39, 43, 29, 60, 42, 21,
20, 59, 57, 58
};
// table of GF(M) elements given their logarithm
static const int qra_exp[qra_M-1] = {
1, 2, 4, 8, 16, 32, 3, 6, 12, 24,
48, 35, 5, 10, 20, 40, 19, 38, 15, 30,
60, 59, 53, 41, 17, 34, 7, 14, 28, 56,
51, 37, 9, 18, 36, 11, 22, 44, 27, 54,
47, 29, 58, 55, 45, 25, 50, 39, 13, 26,
52, 43, 21, 42, 23, 46, 31, 62, 63, 61,
57, 49, 33
};
// table of the messages weight logarithms over GF(M)
static const int qra_msgw[qra_NMSG] = {
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 27, 0, 0, 0, 31,
28, 61, 31, 0, 0, 52, 22, 7, 19, 47,
44, 62, 32, 50, 52, 42, 48, 56, 40, 50,
51, 37, 37, 0, 5, 14, 0, 0, 18, 2,
0, 45, 21, 0, 62, 8, 11, 60, 36, 32,
17, 9, 5, 0, 53, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
};
// table of the degrees of the variable nodes
static const int qra_vdeg[qra_V] = {
4, 4, 4, 4, 5, 5, 5, 5, 7, 4,
4, 6, 8, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3
};
// table of the degrees of the factor nodes
static const int qra_cdeg[qra_C] = {
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 2, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 2
};
// table (uncompressed) of the v->c message indexes (-1=unused entry)
static const int qra_v2cmidx[qra_V*qra_MAXVDEG] = {
0, 68, 104, 112, -1, -1, -1, -1,
1, 73, 101, 111, -1, -1, -1, -1,
2, 74, 84, 95, -1, -1, -1, -1,
3, 66, 78, 87, -1, -1, -1, -1,
4, 65, 76, 85, 97, -1, -1, -1,
5, 79, 88, 96, 109, -1, -1, -1,
6, 70, 93, 102, 110, -1, -1, -1,
7, 75, 83, 94, 103, -1, -1, -1,
8, 71, 81, 91, 99, 107, 115, -1,
9, 67, 80, 92, -1, -1, -1, -1,
10, 86, 105, 113, -1, -1, -1, -1,
11, 69, 77, 89, 100, 108, -1, -1,
12, 64, 72, 82, 90, 98, 106, 114,
13, 116, 117, -1, -1, -1, -1, -1,
14, 118, 119, -1, -1, -1, -1, -1,
15, 120, 121, -1, -1, -1, -1, -1,
16, 122, 123, -1, -1, -1, -1, -1,
17, 124, 125, -1, -1, -1, -1, -1,
18, 126, 127, -1, -1, -1, -1, -1,
19, 128, 129, -1, -1, -1, -1, -1,
20, 130, 131, -1, -1, -1, -1, -1,
21, 132, 133, -1, -1, -1, -1, -1,
22, 134, 135, -1, -1, -1, -1, -1,
23, 136, 137, -1, -1, -1, -1, -1,
24, 138, 139, -1, -1, -1, -1, -1,
25, 140, 141, -1, -1, -1, -1, -1,
26, 142, 143, -1, -1, -1, -1, -1,
27, 144, 145, -1, -1, -1, -1, -1,
28, 146, 147, -1, -1, -1, -1, -1,
29, 148, 149, -1, -1, -1, -1, -1,
30, 150, 151, -1, -1, -1, -1, -1,
31, 152, 153, -1, -1, -1, -1, -1,
32, 154, 155, -1, -1, -1, -1, -1,
33, 156, 157, -1, -1, -1, -1, -1,
34, 158, 159, -1, -1, -1, -1, -1,
35, 160, 161, -1, -1, -1, -1, -1,
36, 162, 163, -1, -1, -1, -1, -1,
37, 164, 165, -1, -1, -1, -1, -1,
38, 166, 167, -1, -1, -1, -1, -1,
39, 168, 169, -1, -1, -1, -1, -1,
40, 170, 171, -1, -1, -1, -1, -1,
41, 172, 173, -1, -1, -1, -1, -1,
42, 174, 175, -1, -1, -1, -1, -1,
43, 176, 177, -1, -1, -1, -1, -1,
44, 178, 179, -1, -1, -1, -1, -1,
45, 180, 181, -1, -1, -1, -1, -1,
46, 182, 183, -1, -1, -1, -1, -1,
47, 184, 185, -1, -1, -1, -1, -1,
48, 186, 187, -1, -1, -1, -1, -1,
49, 188, 189, -1, -1, -1, -1, -1,
50, 190, 191, -1, -1, -1, -1, -1,
51, 192, 193, -1, -1, -1, -1, -1,
52, 194, 195, -1, -1, -1, -1, -1,
53, 196, 197, -1, -1, -1, -1, -1,
54, 198, 199, -1, -1, -1, -1, -1,
55, 200, 201, -1, -1, -1, -1, -1,
56, 202, 203, -1, -1, -1, -1, -1,
57, 204, 205, -1, -1, -1, -1, -1,
58, 206, 207, -1, -1, -1, -1, -1,
59, 208, 209, -1, -1, -1, -1, -1,
60, 210, 211, -1, -1, -1, -1, -1,
61, 212, 213, -1, -1, -1, -1, -1,
62, 214, 215, -1, -1, -1, -1, -1,
63, 216, 217, -1, -1, -1, -1, -1
};
// table (uncompressed) of the c->v message indexes (-1=unused entry)
static const int qra_c2vmidx[qra_C*qra_MAXCDEG] = {
0, -1, -1, 1, -1, -1, 2, -1, -1, 3, -1, -1,
4, -1, -1, 5, -1, -1, 6, -1, -1, 7, -1, -1,
8, -1, -1, 9, -1, -1, 10, -1, -1, 11, -1, -1,
12, -1, -1, 13, -1, -1, 14, -1, -1, 15, -1, -1,
16, -1, -1, 17, -1, -1, 18, -1, -1, 19, -1, -1,
20, -1, -1, 21, -1, -1, 22, -1, -1, 23, -1, -1,
24, -1, -1, 25, -1, -1, 26, -1, -1, 27, -1, -1,
28, -1, -1, 29, -1, -1, 30, -1, -1, 31, -1, -1,
32, -1, -1, 33, -1, -1, 34, -1, -1, 35, -1, -1,
36, -1, -1, 37, -1, -1, 38, -1, -1, 39, -1, -1,
40, -1, -1, 41, -1, -1, 42, -1, -1, 43, -1, -1,
44, -1, -1, 45, -1, -1, 46, -1, -1, 47, -1, -1,
48, -1, -1, 49, -1, -1, 50, -1, -1, 51, -1, -1,
52, -1, -1, 53, -1, -1, 54, -1, -1, 55, -1, -1,
56, -1, -1, 57, -1, -1, 58, -1, -1, 59, -1, -1,
60, -1, -1, 61, -1, -1, 62, -1, -1, 63, -1, -1,
64, 116, -1, 65, 117, 118, 66, 119, 120, 67, 121, 122,
68, 123, 124, 69, 125, 126, 70, 127, 128, 71, 129, 130,
72, 131, 132, 73, 133, 134, 74, 135, 136, 75, 137, 138,
76, 139, 140, 77, 141, 142, 78, 143, 144, 79, 145, 146,
80, 147, 148, 81, 149, 150, 82, 151, 152, 83, 153, 154,
84, 155, 156, 85, 157, 158, 86, 159, 160, 87, 161, 162,
88, 163, 164, 89, 165, 166, 90, 167, 168, 91, 169, 170,
92, 171, 172, 93, 173, 174, 94, 175, 176, 95, 177, 178,
96, 179, 180, 97, 181, 182, 98, 183, 184, 99, 185, 186,
100, 187, 188, 101, 189, 190, 102, 191, 192, 103, 193, 194,
104, 195, 196, 105, 197, 198, 106, 199, 200, 107, 201, 202,
108, 203, 204, 109, 205, 206, 110, 207, 208, 111, 209, 210,
112, 211, 212, 113, 213, 214, 114, 215, 216, 115, 217, -1
};
// permutation matrix to compute Prob(x*alfa^logw)
static const int qra_pmat[qra_M*qra_M] = {
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31,
32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63,
0, 33, 1, 32, 2, 35, 3, 34, 4, 37, 5, 36, 6, 39, 7, 38,
8, 41, 9, 40, 10, 43, 11, 42, 12, 45, 13, 44, 14, 47, 15, 46,
16, 49, 17, 48, 18, 51, 19, 50, 20, 53, 21, 52, 22, 55, 23, 54,
24, 57, 25, 56, 26, 59, 27, 58, 28, 61, 29, 60, 30, 63, 31, 62,
0, 49, 33, 16, 1, 48, 32, 17, 2, 51, 35, 18, 3, 50, 34, 19,
4, 53, 37, 20, 5, 52, 36, 21, 6, 55, 39, 22, 7, 54, 38, 23,
8, 57, 41, 24, 9, 56, 40, 25, 10, 59, 43, 26, 11, 58, 42, 27,
12, 61, 45, 28, 13, 60, 44, 29, 14, 63, 47, 30, 15, 62, 46, 31,
0, 57, 49, 8, 33, 24, 16, 41, 1, 56, 48, 9, 32, 25, 17, 40,
2, 59, 51, 10, 35, 26, 18, 43, 3, 58, 50, 11, 34, 27, 19, 42,
4, 61, 53, 12, 37, 28, 20, 45, 5, 60, 52, 13, 36, 29, 21, 44,
6, 63, 55, 14, 39, 30, 22, 47, 7, 62, 54, 15, 38, 31, 23, 46,
0, 61, 57, 4, 49, 12, 8, 53, 33, 28, 24, 37, 16, 45, 41, 20,
1, 60, 56, 5, 48, 13, 9, 52, 32, 29, 25, 36, 17, 44, 40, 21,
2, 63, 59, 6, 51, 14, 10, 55, 35, 30, 26, 39, 18, 47, 43, 22,
3, 62, 58, 7, 50, 15, 11, 54, 34, 31, 27, 38, 19, 46, 42, 23,
0, 63, 61, 2, 57, 6, 4, 59, 49, 14, 12, 51, 8, 55, 53, 10,
33, 30, 28, 35, 24, 39, 37, 26, 16, 47, 45, 18, 41, 22, 20, 43,
1, 62, 60, 3, 56, 7, 5, 58, 48, 15, 13, 50, 9, 54, 52, 11,
32, 31, 29, 34, 25, 38, 36, 27, 17, 46, 44, 19, 40, 23, 21, 42,
0, 62, 63, 1, 61, 3, 2, 60, 57, 7, 6, 56, 4, 58, 59, 5,
49, 15, 14, 48, 12, 50, 51, 13, 8, 54, 55, 9, 53, 11, 10, 52,
33, 31, 30, 32, 28, 34, 35, 29, 24, 38, 39, 25, 37, 27, 26, 36,
16, 46, 47, 17, 45, 19, 18, 44, 41, 23, 22, 40, 20, 42, 43, 21,
0, 31, 62, 33, 63, 32, 1, 30, 61, 34, 3, 28, 2, 29, 60, 35,
57, 38, 7, 24, 6, 25, 56, 39, 4, 27, 58, 37, 59, 36, 5, 26,
49, 46, 15, 16, 14, 17, 48, 47, 12, 19, 50, 45, 51, 44, 13, 18,
8, 23, 54, 41, 55, 40, 9, 22, 53, 42, 11, 20, 10, 21, 52, 43,
0, 46, 31, 49, 62, 16, 33, 15, 63, 17, 32, 14, 1, 47, 30, 48,
61, 19, 34, 12, 3, 45, 28, 50, 2, 44, 29, 51, 60, 18, 35, 13,
57, 23, 38, 8, 7, 41, 24, 54, 6, 40, 25, 55, 56, 22, 39, 9,
4, 42, 27, 53, 58, 20, 37, 11, 59, 21, 36, 10, 5, 43, 26, 52,
0, 23, 46, 57, 31, 8, 49, 38, 62, 41, 16, 7, 33, 54, 15, 24,
63, 40, 17, 6, 32, 55, 14, 25, 1, 22, 47, 56, 30, 9, 48, 39,
61, 42, 19, 4, 34, 53, 12, 27, 3, 20, 45, 58, 28, 11, 50, 37,
2, 21, 44, 59, 29, 10, 51, 36, 60, 43, 18, 5, 35, 52, 13, 26,
0, 42, 23, 61, 46, 4, 57, 19, 31, 53, 8, 34, 49, 27, 38, 12,
62, 20, 41, 3, 16, 58, 7, 45, 33, 11, 54, 28, 15, 37, 24, 50,
63, 21, 40, 2, 17, 59, 6, 44, 32, 10, 55, 29, 14, 36, 25, 51,
1, 43, 22, 60, 47, 5, 56, 18, 30, 52, 9, 35, 48, 26, 39, 13,
0, 21, 42, 63, 23, 2, 61, 40, 46, 59, 4, 17, 57, 44, 19, 6,
31, 10, 53, 32, 8, 29, 34, 55, 49, 36, 27, 14, 38, 51, 12, 25,
62, 43, 20, 1, 41, 60, 3, 22, 16, 5, 58, 47, 7, 18, 45, 56,
33, 52, 11, 30, 54, 35, 28, 9, 15, 26, 37, 48, 24, 13, 50, 39,
0, 43, 21, 62, 42, 1, 63, 20, 23, 60, 2, 41, 61, 22, 40, 3,
46, 5, 59, 16, 4, 47, 17, 58, 57, 18, 44, 7, 19, 56, 6, 45,
31, 52, 10, 33, 53, 30, 32, 11, 8, 35, 29, 54, 34, 9, 55, 28,
49, 26, 36, 15, 27, 48, 14, 37, 38, 13, 51, 24, 12, 39, 25, 50,
0, 52, 43, 31, 21, 33, 62, 10, 42, 30, 1, 53, 63, 11, 20, 32,
23, 35, 60, 8, 2, 54, 41, 29, 61, 9, 22, 34, 40, 28, 3, 55,
46, 26, 5, 49, 59, 15, 16, 36, 4, 48, 47, 27, 17, 37, 58, 14,
57, 13, 18, 38, 44, 24, 7, 51, 19, 39, 56, 12, 6, 50, 45, 25,
0, 26, 52, 46, 43, 49, 31, 5, 21, 15, 33, 59, 62, 36, 10, 16,
42, 48, 30, 4, 1, 27, 53, 47, 63, 37, 11, 17, 20, 14, 32, 58,
23, 13, 35, 57, 60, 38, 8, 18, 2, 24, 54, 44, 41, 51, 29, 7,
61, 39, 9, 19, 22, 12, 34, 56, 40, 50, 28, 6, 3, 25, 55, 45,
0, 13, 26, 23, 52, 57, 46, 35, 43, 38, 49, 60, 31, 18, 5, 8,
21, 24, 15, 2, 33, 44, 59, 54, 62, 51, 36, 41, 10, 7, 16, 29,
42, 39, 48, 61, 30, 19, 4, 9, 1, 12, 27, 22, 53, 56, 47, 34,
63, 50, 37, 40, 11, 6, 17, 28, 20, 25, 14, 3, 32, 45, 58, 55,
0, 39, 13, 42, 26, 61, 23, 48, 52, 19, 57, 30, 46, 9, 35, 4,
43, 12, 38, 1, 49, 22, 60, 27, 31, 56, 18, 53, 5, 34, 8, 47,
21, 50, 24, 63, 15, 40, 2, 37, 33, 6, 44, 11, 59, 28, 54, 17,
62, 25, 51, 20, 36, 3, 41, 14, 10, 45, 7, 32, 16, 55, 29, 58,
0, 50, 39, 21, 13, 63, 42, 24, 26, 40, 61, 15, 23, 37, 48, 2,
52, 6, 19, 33, 57, 11, 30, 44, 46, 28, 9, 59, 35, 17, 4, 54,
43, 25, 12, 62, 38, 20, 1, 51, 49, 3, 22, 36, 60, 14, 27, 41,
31, 45, 56, 10, 18, 32, 53, 7, 5, 55, 34, 16, 8, 58, 47, 29,
0, 25, 50, 43, 39, 62, 21, 12, 13, 20, 63, 38, 42, 51, 24, 1,
26, 3, 40, 49, 61, 36, 15, 22, 23, 14, 37, 60, 48, 41, 2, 27,
52, 45, 6, 31, 19, 10, 33, 56, 57, 32, 11, 18, 30, 7, 44, 53,
46, 55, 28, 5, 9, 16, 59, 34, 35, 58, 17, 8, 4, 29, 54, 47,
0, 45, 25, 52, 50, 31, 43, 6, 39, 10, 62, 19, 21, 56, 12, 33,
13, 32, 20, 57, 63, 18, 38, 11, 42, 7, 51, 30, 24, 53, 1, 44,
26, 55, 3, 46, 40, 5, 49, 28, 61, 16, 36, 9, 15, 34, 22, 59,
23, 58, 14, 35, 37, 8, 60, 17, 48, 29, 41, 4, 2, 47, 27, 54,
0, 55, 45, 26, 25, 46, 52, 3, 50, 5, 31, 40, 43, 28, 6, 49,
39, 16, 10, 61, 62, 9, 19, 36, 21, 34, 56, 15, 12, 59, 33, 22,
13, 58, 32, 23, 20, 35, 57, 14, 63, 8, 18, 37, 38, 17, 11, 60,
42, 29, 7, 48, 51, 4, 30, 41, 24, 47, 53, 2, 1, 54, 44, 27,
0, 58, 55, 13, 45, 23, 26, 32, 25, 35, 46, 20, 52, 14, 3, 57,
50, 8, 5, 63, 31, 37, 40, 18, 43, 17, 28, 38, 6, 60, 49, 11,
39, 29, 16, 42, 10, 48, 61, 7, 62, 4, 9, 51, 19, 41, 36, 30,
21, 47, 34, 24, 56, 2, 15, 53, 12, 54, 59, 1, 33, 27, 22, 44,
0, 29, 58, 39, 55, 42, 13, 16, 45, 48, 23, 10, 26, 7, 32, 61,
25, 4, 35, 62, 46, 51, 20, 9, 52, 41, 14, 19, 3, 30, 57, 36,
50, 47, 8, 21, 5, 24, 63, 34, 31, 2, 37, 56, 40, 53, 18, 15,
43, 54, 17, 12, 28, 1, 38, 59, 6, 27, 60, 33, 49, 44, 11, 22,
0, 47, 29, 50, 58, 21, 39, 8, 55, 24, 42, 5, 13, 34, 16, 63,
45, 2, 48, 31, 23, 56, 10, 37, 26, 53, 7, 40, 32, 15, 61, 18,
25, 54, 4, 43, 35, 12, 62, 17, 46, 1, 51, 28, 20, 59, 9, 38,
52, 27, 41, 6, 14, 33, 19, 60, 3, 44, 30, 49, 57, 22, 36, 11,
0, 54, 47, 25, 29, 43, 50, 4, 58, 12, 21, 35, 39, 17, 8, 62,
55, 1, 24, 46, 42, 28, 5, 51, 13, 59, 34, 20, 16, 38, 63, 9,
45, 27, 2, 52, 48, 6, 31, 41, 23, 33, 56, 14, 10, 60, 37, 19,
26, 44, 53, 3, 7, 49, 40, 30, 32, 22, 15, 57, 61, 11, 18, 36,
0, 27, 54, 45, 47, 52, 25, 2, 29, 6, 43, 48, 50, 41, 4, 31,
58, 33, 12, 23, 21, 14, 35, 56, 39, 60, 17, 10, 8, 19, 62, 37,
55, 44, 1, 26, 24, 3, 46, 53, 42, 49, 28, 7, 5, 30, 51, 40,
13, 22, 59, 32, 34, 57, 20, 15, 16, 11, 38, 61, 63, 36, 9, 18,
0, 44, 27, 55, 54, 26, 45, 1, 47, 3, 52, 24, 25, 53, 2, 46,
29, 49, 6, 42, 43, 7, 48, 28, 50, 30, 41, 5, 4, 40, 31, 51,
58, 22, 33, 13, 12, 32, 23, 59, 21, 57, 14, 34, 35, 15, 56, 20,
39, 11, 60, 16, 17, 61, 10, 38, 8, 36, 19, 63, 62, 18, 37, 9,
0, 22, 44, 58, 27, 13, 55, 33, 54, 32, 26, 12, 45, 59, 1, 23,
47, 57, 3, 21, 52, 34, 24, 14, 25, 15, 53, 35, 2, 20, 46, 56,
29, 11, 49, 39, 6, 16, 42, 60, 43, 61, 7, 17, 48, 38, 28, 10,
50, 36, 30, 8, 41, 63, 5, 19, 4, 18, 40, 62, 31, 9, 51, 37,
0, 11, 22, 29, 44, 39, 58, 49, 27, 16, 13, 6, 55, 60, 33, 42,
54, 61, 32, 43, 26, 17, 12, 7, 45, 38, 59, 48, 1, 10, 23, 28,
47, 36, 57, 50, 3, 8, 21, 30, 52, 63, 34, 41, 24, 19, 14, 5,
25, 18, 15, 4, 53, 62, 35, 40, 2, 9, 20, 31, 46, 37, 56, 51,
0, 36, 11, 47, 22, 50, 29, 57, 44, 8, 39, 3, 58, 30, 49, 21,
27, 63, 16, 52, 13, 41, 6, 34, 55, 19, 60, 24, 33, 5, 42, 14,
54, 18, 61, 25, 32, 4, 43, 15, 26, 62, 17, 53, 12, 40, 7, 35,
45, 9, 38, 2, 59, 31, 48, 20, 1, 37, 10, 46, 23, 51, 28, 56,
0, 18, 36, 54, 11, 25, 47, 61, 22, 4, 50, 32, 29, 15, 57, 43,
44, 62, 8, 26, 39, 53, 3, 17, 58, 40, 30, 12, 49, 35, 21, 7,
27, 9, 63, 45, 16, 2, 52, 38, 13, 31, 41, 59, 6, 20, 34, 48,
55, 37, 19, 1, 60, 46, 24, 10, 33, 51, 5, 23, 42, 56, 14, 28,
0, 9, 18, 27, 36, 45, 54, 63, 11, 2, 25, 16, 47, 38, 61, 52,
22, 31, 4, 13, 50, 59, 32, 41, 29, 20, 15, 6, 57, 48, 43, 34,
44, 37, 62, 55, 8, 1, 26, 19, 39, 46, 53, 60, 3, 10, 17, 24,
58, 51, 40, 33, 30, 23, 12, 5, 49, 56, 35, 42, 21, 28, 7, 14,
0, 37, 9, 44, 18, 55, 27, 62, 36, 1, 45, 8, 54, 19, 63, 26,
11, 46, 2, 39, 25, 60, 16, 53, 47, 10, 38, 3, 61, 24, 52, 17,
22, 51, 31, 58, 4, 33, 13, 40, 50, 23, 59, 30, 32, 5, 41, 12,
29, 56, 20, 49, 15, 42, 6, 35, 57, 28, 48, 21, 43, 14, 34, 7,
0, 51, 37, 22, 9, 58, 44, 31, 18, 33, 55, 4, 27, 40, 62, 13,
36, 23, 1, 50, 45, 30, 8, 59, 54, 5, 19, 32, 63, 12, 26, 41,
11, 56, 46, 29, 2, 49, 39, 20, 25, 42, 60, 15, 16, 35, 53, 6,
47, 28, 10, 57, 38, 21, 3, 48, 61, 14, 24, 43, 52, 7, 17, 34,
0, 56, 51, 11, 37, 29, 22, 46, 9, 49, 58, 2, 44, 20, 31, 39,
18, 42, 33, 25, 55, 15, 4, 60, 27, 35, 40, 16, 62, 6, 13, 53,
36, 28, 23, 47, 1, 57, 50, 10, 45, 21, 30, 38, 8, 48, 59, 3,
54, 14, 5, 61, 19, 43, 32, 24, 63, 7, 12, 52, 26, 34, 41, 17,
0, 28, 56, 36, 51, 47, 11, 23, 37, 57, 29, 1, 22, 10, 46, 50,
9, 21, 49, 45, 58, 38, 2, 30, 44, 48, 20, 8, 31, 3, 39, 59,
18, 14, 42, 54, 33, 61, 25, 5, 55, 43, 15, 19, 4, 24, 60, 32,
27, 7, 35, 63, 40, 52, 16, 12, 62, 34, 6, 26, 13, 17, 53, 41,
0, 14, 28, 18, 56, 54, 36, 42, 51, 61, 47, 33, 11, 5, 23, 25,
37, 43, 57, 55, 29, 19, 1, 15, 22, 24, 10, 4, 46, 32, 50, 60,
9, 7, 21, 27, 49, 63, 45, 35, 58, 52, 38, 40, 2, 12, 30, 16,
44, 34, 48, 62, 20, 26, 8, 6, 31, 17, 3, 13, 39, 41, 59, 53,
0, 7, 14, 9, 28, 27, 18, 21, 56, 63, 54, 49, 36, 35, 42, 45,
51, 52, 61, 58, 47, 40, 33, 38, 11, 12, 5, 2, 23, 16, 25, 30,
37, 34, 43, 44, 57, 62, 55, 48, 29, 26, 19, 20, 1, 6, 15, 8,
22, 17, 24, 31, 10, 13, 4, 3, 46, 41, 32, 39, 50, 53, 60, 59,
0, 34, 7, 37, 14, 44, 9, 43, 28, 62, 27, 57, 18, 48, 21, 55,
56, 26, 63, 29, 54, 20, 49, 19, 36, 6, 35, 1, 42, 8, 45, 15,
51, 17, 52, 22, 61, 31, 58, 24, 47, 13, 40, 10, 33, 3, 38, 4,
11, 41, 12, 46, 5, 39, 2, 32, 23, 53, 16, 50, 25, 59, 30, 60,
0, 17, 34, 51, 7, 22, 37, 52, 14, 31, 44, 61, 9, 24, 43, 58,
28, 13, 62, 47, 27, 10, 57, 40, 18, 3, 48, 33, 21, 4, 55, 38,
56, 41, 26, 11, 63, 46, 29, 12, 54, 39, 20, 5, 49, 32, 19, 2,
36, 53, 6, 23, 35, 50, 1, 16, 42, 59, 8, 25, 45, 60, 15, 30,
0, 41, 17, 56, 34, 11, 51, 26, 7, 46, 22, 63, 37, 12, 52, 29,
14, 39, 31, 54, 44, 5, 61, 20, 9, 32, 24, 49, 43, 2, 58, 19,
28, 53, 13, 36, 62, 23, 47, 6, 27, 50, 10, 35, 57, 16, 40, 1,
18, 59, 3, 42, 48, 25, 33, 8, 21, 60, 4, 45, 55, 30, 38, 15,
0, 53, 41, 28, 17, 36, 56, 13, 34, 23, 11, 62, 51, 6, 26, 47,
7, 50, 46, 27, 22, 35, 63, 10, 37, 16, 12, 57, 52, 1, 29, 40,
14, 59, 39, 18, 31, 42, 54, 3, 44, 25, 5, 48, 61, 8, 20, 33,
9, 60, 32, 21, 24, 45, 49, 4, 43, 30, 2, 55, 58, 15, 19, 38,
0, 59, 53, 14, 41, 18, 28, 39, 17, 42, 36, 31, 56, 3, 13, 54,
34, 25, 23, 44, 11, 48, 62, 5, 51, 8, 6, 61, 26, 33, 47, 20,
7, 60, 50, 9, 46, 21, 27, 32, 22, 45, 35, 24, 63, 4, 10, 49,
37, 30, 16, 43, 12, 55, 57, 2, 52, 15, 1, 58, 29, 38, 40, 19,
0, 60, 59, 7, 53, 9, 14, 50, 41, 21, 18, 46, 28, 32, 39, 27,
17, 45, 42, 22, 36, 24, 31, 35, 56, 4, 3, 63, 13, 49, 54, 10,
34, 30, 25, 37, 23, 43, 44, 16, 11, 55, 48, 12, 62, 2, 5, 57,
51, 15, 8, 52, 6, 58, 61, 1, 26, 38, 33, 29, 47, 19, 20, 40,
0, 30, 60, 34, 59, 37, 7, 25, 53, 43, 9, 23, 14, 16, 50, 44,
41, 55, 21, 11, 18, 12, 46, 48, 28, 2, 32, 62, 39, 57, 27, 5,
17, 15, 45, 51, 42, 52, 22, 8, 36, 58, 24, 6, 31, 1, 35, 61,
56, 38, 4, 26, 3, 29, 63, 33, 13, 19, 49, 47, 54, 40, 10, 20,
0, 15, 30, 17, 60, 51, 34, 45, 59, 52, 37, 42, 7, 8, 25, 22,
53, 58, 43, 36, 9, 6, 23, 24, 14, 1, 16, 31, 50, 61, 44, 35,
41, 38, 55, 56, 21, 26, 11, 4, 18, 29, 12, 3, 46, 33, 48, 63,
28, 19, 2, 13, 32, 47, 62, 49, 39, 40, 57, 54, 27, 20, 5, 10,
0, 38, 15, 41, 30, 56, 17, 55, 60, 26, 51, 21, 34, 4, 45, 11,
59, 29, 52, 18, 37, 3, 42, 12, 7, 33, 8, 46, 25, 63, 22, 48,
53, 19, 58, 28, 43, 13, 36, 2, 9, 47, 6, 32, 23, 49, 24, 62,
14, 40, 1, 39, 16, 54, 31, 57, 50, 20, 61, 27, 44, 10, 35, 5,
0, 19, 38, 53, 15, 28, 41, 58, 30, 13, 56, 43, 17, 2, 55, 36,
60, 47, 26, 9, 51, 32, 21, 6, 34, 49, 4, 23, 45, 62, 11, 24,
59, 40, 29, 14, 52, 39, 18, 1, 37, 54, 3, 16, 42, 57, 12, 31,
7, 20, 33, 50, 8, 27, 46, 61, 25, 10, 63, 44, 22, 5, 48, 35,
0, 40, 19, 59, 38, 14, 53, 29, 15, 39, 28, 52, 41, 1, 58, 18,
30, 54, 13, 37, 56, 16, 43, 3, 17, 57, 2, 42, 55, 31, 36, 12,
60, 20, 47, 7, 26, 50, 9, 33, 51, 27, 32, 8, 21, 61, 6, 46,
34, 10, 49, 25, 4, 44, 23, 63, 45, 5, 62, 22, 11, 35, 24, 48,
0, 20, 40, 60, 19, 7, 59, 47, 38, 50, 14, 26, 53, 33, 29, 9,
15, 27, 39, 51, 28, 8, 52, 32, 41, 61, 1, 21, 58, 46, 18, 6,
30, 10, 54, 34, 13, 25, 37, 49, 56, 44, 16, 4, 43, 63, 3, 23,
17, 5, 57, 45, 2, 22, 42, 62, 55, 35, 31, 11, 36, 48, 12, 24,
0, 10, 20, 30, 40, 34, 60, 54, 19, 25, 7, 13, 59, 49, 47, 37,
38, 44, 50, 56, 14, 4, 26, 16, 53, 63, 33, 43, 29, 23, 9, 3,
15, 5, 27, 17, 39, 45, 51, 57, 28, 22, 8, 2, 52, 62, 32, 42,
41, 35, 61, 55, 1, 11, 21, 31, 58, 48, 46, 36, 18, 24, 6, 12,
0, 5, 10, 15, 20, 17, 30, 27, 40, 45, 34, 39, 60, 57, 54, 51,
19, 22, 25, 28, 7, 2, 13, 8, 59, 62, 49, 52, 47, 42, 37, 32,
38, 35, 44, 41, 50, 55, 56, 61, 14, 11, 4, 1, 26, 31, 16, 21,
53, 48, 63, 58, 33, 36, 43, 46, 29, 24, 23, 18, 9, 12, 3, 6,
0, 35, 5, 38, 10, 41, 15, 44, 20, 55, 17, 50, 30, 61, 27, 56,
40, 11, 45, 14, 34, 1, 39, 4, 60, 31, 57, 26, 54, 21, 51, 16,
19, 48, 22, 53, 25, 58, 28, 63, 7, 36, 2, 33, 13, 46, 8, 43,
59, 24, 62, 29, 49, 18, 52, 23, 47, 12, 42, 9, 37, 6, 32, 3,
0, 48, 35, 19, 5, 53, 38, 22, 10, 58, 41, 25, 15, 63, 44, 28,
20, 36, 55, 7, 17, 33, 50, 2, 30, 46, 61, 13, 27, 43, 56, 8,
40, 24, 11, 59, 45, 29, 14, 62, 34, 18, 1, 49, 39, 23, 4, 52,
60, 12, 31, 47, 57, 9, 26, 42, 54, 6, 21, 37, 51, 3, 16, 32,
0, 24, 48, 40, 35, 59, 19, 11, 5, 29, 53, 45, 38, 62, 22, 14,
10, 18, 58, 34, 41, 49, 25, 1, 15, 23, 63, 39, 44, 52, 28, 4,
20, 12, 36, 60, 55, 47, 7, 31, 17, 9, 33, 57, 50, 42, 2, 26,
30, 6, 46, 54, 61, 37, 13, 21, 27, 3, 43, 51, 56, 32, 8, 16,
0, 12, 24, 20, 48, 60, 40, 36, 35, 47, 59, 55, 19, 31, 11, 7,
5, 9, 29, 17, 53, 57, 45, 33, 38, 42, 62, 50, 22, 26, 14, 2,
10, 6, 18, 30, 58, 54, 34, 46, 41, 37, 49, 61, 25, 21, 1, 13,
15, 3, 23, 27, 63, 51, 39, 43, 44, 32, 52, 56, 28, 16, 4, 8,
0, 6, 12, 10, 24, 30, 20, 18, 48, 54, 60, 58, 40, 46, 36, 34,
35, 37, 47, 41, 59, 61, 55, 49, 19, 21, 31, 25, 11, 13, 7, 1,
5, 3, 9, 15, 29, 27, 17, 23, 53, 51, 57, 63, 45, 43, 33, 39,
38, 32, 42, 44, 62, 56, 50, 52, 22, 16, 26, 28, 14, 8, 2, 4,
0, 3, 6, 5, 12, 15, 10, 9, 24, 27, 30, 29, 20, 23, 18, 17,
48, 51, 54, 53, 60, 63, 58, 57, 40, 43, 46, 45, 36, 39, 34, 33,
35, 32, 37, 38, 47, 44, 41, 42, 59, 56, 61, 62, 55, 52, 49, 50,
19, 16, 21, 22, 31, 28, 25, 26, 11, 8, 13, 14, 7, 4, 1, 2,
0, 32, 3, 35, 6, 38, 5, 37, 12, 44, 15, 47, 10, 42, 9, 41,
24, 56, 27, 59, 30, 62, 29, 61, 20, 52, 23, 55, 18, 50, 17, 49,
48, 16, 51, 19, 54, 22, 53, 21, 60, 28, 63, 31, 58, 26, 57, 25,
40, 8, 43, 11, 46, 14, 45, 13, 36, 4, 39, 7, 34, 2, 33, 1,
0, 16, 32, 48, 3, 19, 35, 51, 6, 22, 38, 54, 5, 21, 37, 53,
12, 28, 44, 60, 15, 31, 47, 63, 10, 26, 42, 58, 9, 25, 41, 57,
24, 8, 56, 40, 27, 11, 59, 43, 30, 14, 62, 46, 29, 13, 61, 45,
20, 4, 52, 36, 23, 7, 55, 39, 18, 2, 50, 34, 17, 1, 49, 33,
0, 8, 16, 24, 32, 40, 48, 56, 3, 11, 19, 27, 35, 43, 51, 59,
6, 14, 22, 30, 38, 46, 54, 62, 5, 13, 21, 29, 37, 45, 53, 61,
12, 4, 28, 20, 44, 36, 60, 52, 15, 7, 31, 23, 47, 39, 63, 55,
10, 2, 26, 18, 42, 34, 58, 50, 9, 1, 25, 17, 41, 33, 57, 49,
0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60,
3, 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63,
6, 2, 14, 10, 22, 18, 30, 26, 38, 34, 46, 42, 54, 50, 62, 58,
5, 1, 13, 9, 21, 17, 29, 25, 37, 33, 45, 41, 53, 49, 61, 57,
0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30,
32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62,
3, 1, 7, 5, 11, 9, 15, 13, 19, 17, 23, 21, 27, 25, 31, 29,
35, 33, 39, 37, 43, 41, 47, 45, 51, 49, 55, 53, 59, 57, 63, 61
};
const qracode qra_13_64_64_irr_e = {
qra_K,
qra_N,
qra_m,
qra_M,
qra_a,
qra_NC,
qra_V,
qra_C,
qra_NMSG,
qra_MAXVDEG,
qra_MAXCDEG,
QRATYPE_CRCPUNCTURED,
qra_R,
CODE_NAME,
qra_acc_input_idx,
qra_acc_input_wlog,
qra_log,
qra_exp,
qra_msgw,
qra_vdeg,
qra_cdeg,
qra_v2cmidx,
qra_c2vmidx,
qra_pmat
};
#undef qra_K
#undef qra_N
#undef qra_m
#undef qra_M
#undef qra_a
#undef qra_NC
#undef qra_V
#undef qra_C
#undef qra_NMSG
#undef qra_MAXVDEG
#undef qra_MAXCDEG
#undef qra_R
#undef CODE_NAME

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// qra13_64_64_irr_e.h
// Code tables and defines for Q-ary RA code (13,64) over GF(64)
// Code Name: qra13_64_64_irr_e
// (13,64) RA Code over GF(64) RF=[3x4 4x4 6x1 3x2 5x1 7x1]/18
// (c) 2016 - Nico Palermo - IV3NWV - Microtelecom Srl, Italy
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#ifndef _qra13_64_64_irr_e_h
#define _qra13_64_64_irr_e_h
#include "qracodes.h"
#ifdef __cplusplus
extern "C" {
#endif
extern const qracode qra_13_64_64_irr_e;
#ifdef __cplusplus
}
#endif
#endif // _qra13_64_64_irr_e_h

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// qracodes.c
// Q-ary RA codes encoding/decoding functions
//
// (c) 2016 - Nico Palermo, IV3NWV - Microtelecom Srl, Italy
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#include <stdio.h>
#include <math.h>
#include "npfwht.h"
#include "pdmath.h"
#include "qracodes.h"
int qra_encode(const qracode *pcode, int *y, const int *x)
{
int k,j,kk,jj;
int t, chk = 0;
const int K = pcode->K;
const int M = pcode->M;
const int NC= pcode->NC;
const int a = pcode->a;
const int *acc_input_idx = pcode->acc_input_idx;
const int *acc_input_wlog = pcode->acc_input_wlog;
const int *gflog = pcode->gflog;
const int *gfexp = pcode->gfexp;
// copy the systematic symbols to destination
memcpy(y,x,K*sizeof(int));
y = y+K; // point to check symbols
// compute the code check symbols as a weighted accumulation of a permutated
// sequence of the (repeated) systematic input symbols:
// chk(k+1) = x(idx(k))*alfa^(logw(k)) + chk(k)
// (all operations performed over GF(M))
if (a==1) { // grouping factor = 1
for (k=0;k<NC;k++) {
t = x[acc_input_idx[k]];
if (t) {
// multiply input by weight[k] and xor it with previous check
t = (gflog[t] + acc_input_wlog[k])%(M-1);
t = gfexp[t];
chk ^=t;
}
y[k] = chk;
}
#ifdef QRA_DEBUG
// verify that the encoder accumulator is terminated to 0
// (we designed the code this way so that Iex = 1 when Ia = 1)
t = x[acc_input_idx[k]];
if (t) {
t = (gflog[t] + acc_input_wlog[k])%(M-1);
t = gfexp[t];
// accumulation
chk ^=t;
}
return (chk==0);
#else
return 1;
#endif // QRA_DEBUG
}
else { // grouping factor > 1
for (k=0;k<NC;k++) {
kk = a*k;
for (j=0;j<a;j++) {
jj = kk+j;
// irregular grouping support
if (acc_input_idx[jj]<0)
continue;
t = x[acc_input_idx[jj]];
if (t) {
// multiply input by weight[k] and xor it with previous check
t = (gflog[t] + acc_input_wlog[jj])%(M-1);
t = gfexp[t];
chk ^=t;
}
}
y[k] = chk;
}
#ifdef QRA_DEBUG
// verify that the encoder accumulator is terminated to 0
// (we designed the code this way so that Iex = 1 when Ia = 1)
kk = a*k;
for (j=0;j<a;j++) {
jj = kk+j;
if (acc_input_idx[jj]<0)
continue;
t = x[acc_input_idx[jj]];
if (t) {
// multiply input by weight[k] and xor it with previous check
t = (gflog[t] + acc_input_wlog[jj])%(M-1);
t = gfexp[t];
chk ^=t;
}
}
return (chk==0);
#else
return 1;
#endif // QRA_DEBUG
}
}
static void qra_ioapprox(float *src, float C, int nitems)
{
// In place approximation of the modified bessel function I0(x*C)
// Computes src[k] = Io(src[k]*C) where Io() is the modified Bessel function of first kind and order 0
float v;
float vsq;
while (nitems--) {
v = src[nitems]*C;
// rational approximation of log(Io(v))
vsq = v*v;
v = vsq*(v+0.039f)/(vsq*.9931f+v*2.6936f+0.5185f);
if (v>80.f) // avoid floating point exp() overflows
v=80.f;
src[nitems] = (float)exp(v);
}
}
float qra_mfskbesselmetric(float *pix, const float *rsq, const int m, const int N, float EsNoMetric)
{
// Computes the codeword symbols intrinsic probabilities
// given the square of the received input amplitudes.
// The input vector rqs must be a linear array of size M*N, where M=2^m,
// containing the squared amplitudes (rp*rp+rq*rq) of the input samples
// First symbol amplitudes should be stored in the first M positions,
// second symbol amplitudes stored at positions [M ... 2*M-1], and so on.
// Output vector is the intrinsic symbol metric (the probability distribution)
// assuming that symbols are transmitted using a M-FSK modulation
// and incoherent demodulation.
// As the input Es/No is generally unknown (as it cannot be exstimated accurately
// when the codeword length is few tens symbols) but an exact metric requires it
// we simply fix it to a predefined EsNoMetric value so that the metric is what
// expected at that specific value.
// The metric computed in this way is optimal only at this predefined Es/No value,
// nevertheless it is usually better than a generic parameter-free metric which
// makes no assumptions on the input Es/No.
// returns the estimated noise standard deviation
int k;
float rsum = 0.f;
float sigmaest, cmetric;
const int M = 1<<m;
const int nsamples = M*N;
// compute total power and modulus of input signal
for (k=0;k<nsamples;k++) {
rsum = rsum+rsq[k];
pix[k] = (float)sqrt(rsq[k]);
}
rsum = rsum/nsamples; // average S+N
// IMPORTANT NOTE: in computing the noise stdev it is assumed that
// in the input amplitudes there's no strong interference!
// A more robust estimation can be done evaluating the histogram of the input amplitudes
sigmaest = (float)sqrt(rsum/(1.0f+EsNoMetric/M)/2); // estimated noise stdev
cmetric = (float)sqrt(2*EsNoMetric)/sigmaest;
for (k=0;k<N;k++) {
// compute bessel metric for each symbol in the codeword
qra_ioapprox(PD_ROWADDR(pix,M,k),cmetric,M);
// normalize to a probability distribution
pd_norm(PD_ROWADDR(pix,M,k),m);
}
return sigmaest;
}
#ifdef QRA_DEBUG
void pd_print(int imsg,float *ppd,int size)
{
int k;
printf("imsg=%d\n",imsg);
for (k=0;k<size;k++)
printf("%7.1e ",ppd[k]);
printf("\n");
}
#endif
#define ADDRMSG(fp, msgidx) PD_ROWADDR(fp,qra_M,msgidx)
#define C2VMSG(msgidx) PD_ROWADDR(qra_c2vmsg,qra_M,msgidx)
#define V2CMSG(msgidx) PD_ROWADDR(qra_v2cmsg,qra_M,msgidx)
#define MSGPERM(logw) PD_ROWADDR(qra_pmat,qra_M,logw)
#define QRACODE_MAX_M 256 // Maximum alphabet size handled by qra_extrinsic
int qra_extrinsic(const qracode *pcode,
float *pex,
const float *pix,
int maxiter,
float *qra_v2cmsg,
float *qra_c2vmsg)
{
const int qra_M = pcode->M;
const int qra_m = pcode->m;
const int qra_V = pcode->V;
const int qra_MAXVDEG = pcode->MAXVDEG;
const int *qra_vdeg = pcode->vdeg;
const int qra_C = pcode->C;
const int qra_MAXCDEG = pcode->MAXCDEG;
const int *qra_cdeg = pcode->cdeg;
const int *qra_v2cmidx = pcode->v2cmidx;
const int *qra_c2vmidx = pcode->c2vmidx;
const int *qra_pmat = pcode->gfpmat;
const int *qra_msgw = pcode->msgw;
// float msgout[qra_M]; // buffer to store temporary results
float msgout[QRACODE_MAX_M]; // we use a fixed size in order to avoid mallocs
float totex; // total extrinsic information
int nit; // current iteration
int nv; // current variable
int nc; // current check
int k,kk; // loop indexes
int ndeg; // current node degree
int msgbase; // current offset in the table of msg indexes
int imsg; // current message index
int wmsg; // current message weight
int rc = -1; // rc>=0 extrinsic converged to 1 at iteration rc (rc=0..maxiter-1)
// rc=-1 no convergence in the given number of iterations
// rc=-2 error in the code tables (code checks degrees must be >1)
// rc=-3 M is larger than QRACODE_MAX_M
if (qra_M>QRACODE_MAX_M)
return -3;
// message initialization -------------------------------------------------------
// init c->v variable intrinsic msgs
pd_init(C2VMSG(0),pix,qra_M*qra_V);
// init the v->c messages directed to code factors (k=1..ndeg) with the intrinsic info
for (nv=0;nv<qra_V;nv++) {
ndeg = qra_vdeg[nv]; // degree of current node
msgbase = nv*qra_MAXVDEG; // base to msg index row for the current node
// copy intrinsics on v->c
for (k=1;k<ndeg;k++) {
imsg = qra_v2cmidx[msgbase+k];
pd_init(V2CMSG(imsg),ADDRMSG(pix,nv),qra_M);
}
}
// message passing algorithm iterations ------------------------------
for (nit=0;nit<maxiter;nit++) {
// c->v step -----------------------------------------------------
// Computes messages from code checks to code variables.
// As the first qra_V checks are associated with intrinsic information
// (the code tables have been constructed in this way)
// we need to do this step only for code checks in the range [qra_V..qra_C)
// The convolutions of probability distributions over the alphabet of a finite field GF(qra_M)
// are performed with a fast convolution algorithm over the given field.
//
// I.e. given the code check x1+x2+x3 = 0 (with x1,x2,x3 in GF(2^m))
// and given Prob(x2) and Prob(x3), we have that:
// Prob(x1=X1) = Prob((x2+x3)=X1) = sum((Prob(x2=X2)*Prob(x3=(X1+X2))) for all the X2s in the field
// This translates to Prob(x1) = IWHT(WHT(Prob(x2))*WHT(Prob(x3)))
// where WHT and IWHT are the direct and inverse Walsh-Hadamard transforms of the argument.
// Note that the WHT and the IWHF differs only by a multiplicative coefficent and since in this step
// we don't need that the output distribution is normalized we use the relationship
// Prob(x1) =(proportional to) WH(WH(Prob(x2))*WH(Prob(x3)))
// In general given the check code x1+x2+x3+..+xm = 0
// the output distribution of a variable given the distributions of the other m-1 variables
// is the inverse WHT of the product of the WHTs of the distribution of the other m-1 variables
// The complexity of this algorithm scales with M*log2(M) instead of the M^2 complexity of
// the brute force approach (M=size of the alphabet)
for (nc=qra_V;nc<qra_C;nc++) {
ndeg = qra_cdeg[nc]; // degree of current node
if (ndeg==1) // this should never happen (code factors must have deg>1)
return -2; // bad code tables
msgbase = nc*qra_MAXCDEG; // base to msg index row for the current node
// transforms inputs in the Walsh-Hadamard "frequency" domain
// v->c -> fwht(v->c)
for (k=0;k<ndeg;k++) {
imsg = qra_c2vmidx[msgbase+k]; // msg index
np_fwht(qra_m,V2CMSG(imsg),V2CMSG(imsg)); // compute fwht
}
// compute products and transform them back in the WH "time" domain
for (k=0;k<ndeg;k++) {
// init output message to uniform distribution
pd_init(msgout,pd_uniform(qra_m),qra_M);
// c->v = prod(fwht(v->c))
// TODO: we assume that checks degrees are not larger than three but
// if they are larger the products can be computed more efficiently
for (kk=0;kk<ndeg;kk++)
if (kk!=k) {
imsg = qra_c2vmidx[msgbase+kk];
pd_imul(msgout,V2CMSG(imsg),qra_m);
}
// transform product back in the WH "time" domain
// Very important trick:
// we bias WHT[0] so that the sum of output pd components is always strictly positive
// this helps avoiding the effects of underflows in the v->c steps when multipling
// small fp numbers
msgout[0]+=1E-7f; // TODO: define the bias accordingly to the field size
np_fwht(qra_m,msgout,msgout);
// inverse weight and output
imsg = qra_c2vmidx[msgbase+k]; // current output msg index
wmsg = qra_msgw[imsg]; // current msg weight
if (wmsg==0)
pd_init(C2VMSG(imsg),msgout,qra_M);
else
// output p(alfa^(-w)*x)
pd_bwdperm(C2VMSG(imsg),msgout, MSGPERM(wmsg), qra_M);
} // for (k=0;k<ndeg;k++)
} // for (nc=qra_V;nc<qra_C;nc++)
// v->c step -----------------------------------------------------
for (nv=0;nv<qra_V;nv++) {
ndeg = qra_vdeg[nv]; // degree of current node
msgbase = nv*qra_MAXVDEG; // base to msg index row for the current node
for (k=0;k<ndeg;k++) {
// init output message to uniform distribution
pd_init(msgout,pd_uniform(qra_m),qra_M);
// v->c msg = prod(c->v)
// TODO: factor factors to reduce the number of computations for high degree nodes
for (kk=0;kk<ndeg;kk++)
if (kk!=k) {
imsg = qra_v2cmidx[msgbase+kk];
pd_imul(msgout,C2VMSG(imsg),qra_m);
}
#ifdef QRA_DEBUG
// normalize and check if product of messages v->c are null
// normalize output to a probability distribution
if (pd_norm(msgout,qra_m)<=0) {
// dump msgin;
printf("warning: v->c pd with invalid norm. nit=%d nv=%d k=%d\n",nit,nv,k);
for (kk=0;kk<ndeg;kk++) {
imsg = qra_v2cmidx[msgbase+kk];
pd_print(imsg,C2VMSG(imsg),qra_M);
}
printf("-----------------\n");
}
#else
// normalize the result to a probability distribution
pd_norm(msgout,qra_m);
#endif
// weight and output
imsg = qra_v2cmidx[msgbase+k]; // current output msg index
wmsg = qra_msgw[imsg]; // current msg weight
if (wmsg==0) {
pd_init(V2CMSG(imsg),msgout,qra_M);
}
else {
// output p(alfa^w*x)
pd_fwdperm(V2CMSG(imsg),msgout, MSGPERM(wmsg), qra_M);
}
} // for (k=0;k<ndeg;k++)
} // for (nv=0;nv<qra_V;nv++)
// check extrinsic information ------------------------------
// We assume that decoding is successful if each of the extrinsic
// symbol probability is close to ej, where ej = [0 0 0 1(j-th position) 0 0 0 ]
// Therefore, for each symbol k in the codeword we compute max(prob(Xk))
// and we stop the iterations if sum(max(prob(xk)) is close to the codeword length
// Note: this is a more restrictive criterium than that of computing the a
// posteriori probability of each symbol, making a hard decision and then check
// if the codeword syndrome is null.
// WARNING: this is tricky and probably works only for the particular class of RA codes
// we are coping with (we designed the code weights so that for any input symbol the
// sum of its weigths is always 0, thus terminating the accumulator trellis to zero
// for every combination of the systematic symbols).
// More generally we should instead compute the max a posteriori probabilities
// (as a product of the intrinsic and extrinsic information), make a symbol by symbol hard
// decision and then check that the syndrome of the result is indeed null.
totex = 0;
for (nv=0;nv<qra_V;nv++)
totex += pd_max(V2CMSG(nv),qra_M);
if (totex>(1.*(qra_V)-0.01)) {
// the total maximum extrinsic information of each symbol in the codeword
// is very close to one. This means that we have reached the (1,1) point in the
// code EXIT chart(s) and we have successfully decoded the input.
rc = nit;
break; // remove the break to evaluate the decoder speed performance as a function of the max iterations number)
}
} // for (nit=0;nit<maxiter;nit++)
// copy extrinsic information to output to do the actual max a posteriori prob decoding
pd_init(pex,V2CMSG(0),(qra_M*qra_V));
return rc;
}
void qra_mapdecode(const qracode *pcode, int *xdec, float *pex, const float *pix)
{
// Maximum a posteriori probability decoding.
// Given the intrinsic information (pix) and extrinsic information (pex) (computed with qra_extrinsic(...))
// compute pmap = pex*pix and decode each (information) symbol of the received codeword
// as the symbol which maximizes pmap
// Returns:
// xdec[k] = decoded (information) symbols k=[0..qra_K-1]
// Note: pex is destroyed and overwritten with mapp
const int qra_M = pcode->M;
const int qra_m = pcode->m;
const int qra_K = pcode->K;
int k;
for (k=0;k<qra_K;k++) {
// compute a posteriori prob
pd_imul(PD_ROWADDR(pex,qra_M,k),PD_ROWADDR(pix,qra_M,k),qra_m);
xdec[k]=pd_argmax(NULL, PD_ROWADDR(pex,qra_M,k), qra_M);
}
}

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// qracodes.h
// Q-ary RA codes encoding/decoding functions
//
// (c) 2016 - Nico Palermo, IV3NWV - Microtelecom Srl, Italy
// ------------------------------------------------------------------------------
// This file is part of the qracodes project, a Forward Error Control
// encoding/decoding package based on Q-ary RA (Repeat and Accumulate) LDPC codes.
//
// qracodes is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// qracodes is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with qracodes source distribution.
// If not, see <http://www.gnu.org/licenses/>.
#ifndef _qracodes_h_
#define _qracodes_h_
// type of codes
#define QRATYPE_NORMAL 0x00 // normal code
#define QRATYPE_CRC 0x01 // code with crc - last information symbol is a CRC
#define QRATYPE_CRCPUNCTURED 0x02 // the CRC symbol is punctured (not sent along the channel)
typedef struct {
// code parameters
const int K; // number of information symbols
const int N; // codeword length in symbols
const int m; // bits/symbol
const int M; // Symbol alphabet cardinality (2^m)
const int a; // code grouping factor
const int NC; // number of check symbols (N-K)
const int V; // number of variables in the code graph (N)
const int C; // number of factors in the code graph (N +(N-K)+1)
const int NMSG; // number of msgs in the code graph
const int MAXVDEG; // maximum variable degree
const int MAXCDEG; // maximum factor degree
const int type; // see QRATYPE_xx defines
const float R; // code rate (K/N)
const char name[64]; // code name
// tables used by the encoder
const int *acc_input_idx;
const int *acc_input_wlog;
const int *gflog;
const int *gfexp;
// tables used by the decoder -------------------------
const int *msgw;
const int *vdeg;
const int *cdeg;
const int *v2cmidx;
const int *c2vmidx;
const int *gfpmat;
} qracode;
// Uncomment the header file of the code which needs to be tested
//#include "qra12_63_64_irr_b.h" // irregular code (12,63) over GF(64)
//#include "qra13_64_64_irr_e.h" // irregular code with good performance and best UER protection at AP56
//#include "qra13_64_64_reg_a.h" // regular code with good UER but perf. inferior to that of code qra12_63_64_irr_b
#ifdef __cplusplus
extern "C" {
#endif
int qra_encode(const qracode *pcode, int *y, const int *x);
float qra_mfskbesselmetric(float *pix, const float *rsq, const int m, const int N, float EsNoMetric);
int qra_extrinsic(const qracode *pcode, float *pex, const float *pix, int maxiter,float *qra_v2cmsg,float *qra_c2vmsg);
void qra_mapdecode(const qracode *pcode, int *xdec, float *pex, const float *pix);
#ifdef __cplusplus
}
#endif
#endif // _qracodes_h_