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sdrangel/ft8/libldpc.cpp

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///////////////////////////////////////////////////////////////////////////////////
// Copyright (C) 2023 Edouard Griffiths, F4EXB <f4exb06@gmail.com> //
// //
// This is the code from ft8mon: https://github.com/rtmrtmrtmrtm/ft8mon //
// reformatted and adapted to Qt and SDRangel context //
// //
// This program 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 as version 3 of the License, or //
// (at your option) any later version. //
// //
// This program 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 V3 for more details. //
// //
// You should have received a copy of the GNU General Public License //
// along with this program. If not, see <http://www.gnu.org/licenses/>. //
///////////////////////////////////////////////////////////////////////////////////
//
// Low Density Parity Check (LDPC) decoder for new FT8.
//
// given a 174-bit codeword as an array of log-likelihood of zero,
// return a 174-bit corrected codeword, or zero-length array.
// first 91 bits are the (systematic) plain-text.
// codeword[i] = log ( P(x=0) / P(x=1) )
//
// this is an implementation of the sum-product algorithm
// from Sarah Johnson's Iterative Error Correction book, and
// Bernhard Leiner's http://www.bernh.net/media/download/papers/ldpc.pdf
//
// cc -O3 libldpc.c -shared -fPIC -o libldpc.so
//
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include "arrays.h"
#include "libldpc.h"
// float, long float, __float128
#define REAL float
namespace FT8
{
//
// does a 174-bit codeword pass the FT8's LDPC parity checks?
// returns the number of parity checks that passed.
// 83 means total success.
//
int LDPC::ldpc_check(int codeword[])
{
int score = 0;
// Nm[83][7]
for (int j = 0; j < 83; j++)
{
int x = 0;
for (int ii1 = 0; ii1 < 7; ii1++)
{
int i1 = Arrays::Nm[j][ii1] - 1;
if (i1 >= 0)
{
x ^= codeword[i1];
}
}
if (x == 0)
score++;
}
return score;
}
// llcodeword is 174 log-likelihoods.
// plain is a return value, 174 ints, to be 0 or 1.
// iters is how hard to try.
// ok is the number of parity checks that worked out,
// ok == 83 means success.
void LDPC::ldpc_decode(float llcodeword[], int iters, int plain[], int *ok)
{
REAL m[83][174];
REAL e[83][174];
REAL codeword[174];
int best_score = -1;
int best_cw[174];
// to translate from log-likelihood x to probability p,
// p = e**x / (1 + e**x)
// it's P(zero), not P(one).
for (int i = 0; i < 174; i++)
{
REAL ex = expl(llcodeword[i]);
REAL p = ex / (1.0 + ex);
codeword[i] = p;
}
// m[j][i] tells the j'th check bit the P(zero) of
// each of its codeword inputs, based on check
// bits other than j.
for (int i = 0; i < 174; i++)
for (int j = 0; j < 83; j++)
m[j][i] = codeword[i];
// e[j][i]: each check j tells each codeword bit i the
// probability of the bit being zero based
// on the *other* bits contributing to that check.
for (int i = 0; i < 174; i++)
for (int j = 0; j < 83; j++)
e[j][i] = 0.0;
for (int iter = 0; iter < iters; iter++)
{
for (int j = 0; j < 83; j++)
{
for (int ii1 = 0; ii1 < 7; ii1++)
{
int i1 = Arrays::Nm[j][ii1] - 1;
if (i1 < 0)
continue;
REAL a = 1.0;
for (int ii2 = 0; ii2 < 7; ii2++)
{
int i2 = Arrays::Nm[j][ii2] - 1;
if (i2 >= 0 && i2 != i1)
{
// tmp ranges from 1.0 to -1.0, for
// definitely zero to definitely one.
float tmp = 1.0 - 2.0 * (1.0 - m[j][i2]);
a *= tmp;
}
}
// a ranges from 1.0 to -1.0, meaning
// bit i1 should be zero .. one.
// so e[j][i1] will be 0.0 .. 1.0 meaning
// bit i1 is one .. zero.
REAL tmp = 0.5 + 0.5 * a;
e[j][i1] = tmp;
}
}
int cw[174];
for (int i = 0; i < 174; i++)
{
REAL q0 = codeword[i];
REAL q1 = 1.0 - q0;
for (int j = 0; j < 3; j++)
{
int j2 = Arrays::Mn[i][j] - 1;
q0 *= e[j2][i];
q1 *= 1.0 - e[j2][i];
}
// REAL p = q0 / (q0 + q1);
REAL p;
if (q0 == 0.0)
{
p = 1.0;
}
else
{
p = 1.0 / (1.0 + (q1 / q0));
}
cw[i] = (p <= 0.5);
}
int score = ldpc_check(cw);
if (score == 83)
{
for (int i = 0; i < 174; i++)
plain[i] = cw[i];
*ok = 83;
return;
}
if (score > best_score)
{
for (int i = 0; i < 174; i++)
best_cw[i] = cw[i];
best_score = score;
}
for (int i = 0; i < 174; i++)
{
for (int ji1 = 0; ji1 < 3; ji1++)
{
int j1 = Arrays::Mn[i][ji1] - 1;
REAL q0 = codeword[i];
REAL q1 = 1.0 - q0;
for (int ji2 = 0; ji2 < 3; ji2++)
{
int j2 = Arrays::Mn[i][ji2] - 1;
if (j1 != j2)
{
q0 *= e[j2][i];
q1 *= 1.0 - e[j2][i];
}
}
// REAL p = q0 / (q0 + q1);
REAL p;
if (q0 == 0.0)
{
p = 1.0;
}
else
{
p = 1.0 / (1.0 + (q1 / q0));
}
m[j1][i] = p;
}
}
}
// decode didn't work, return best guess.
for (int i = 0; i < 174; i++)
plain[i] = best_cw[i];
*ok = best_score;
}
// thank you Douglas Bagnall
// https://math.stackexchange.com/a/446411
float LDPC::fast_tanh(float x)
{
if (x < -7.6)
{
return -0.999;
}
if (x > 7.6)
{
return 0.999;
}
float x2 = x * x;
float a = x * (135135.0f + x2 * (17325.0f + x2 * (378.0f + x2)));
float b = 135135.0f + x2 * (62370.0f + x2 * (3150.0f + x2 * 28.0f));
return a / b;
}
#if 0
#define TANGRAN 0.01
static float tanhtable[];
float
table_tanh(float x)
{
int ind = (x - (-5.0)) / TANGRAN;
if(ind < 0){
return -1.0;
}
if(ind >= 1000){
return 1.0;
}
return tanhtable[ind];
}
#endif
// codeword is 174 log-likelihoods.
// plain is a return value, 174 ints, to be 0 or 1.
// iters is how hard to try.
// ok is the number of parity checks that worked out,
// ok == 83 means success.
void LDPC::ldpc_decode_log(float codeword[], int iters, int plain[], int *ok)
{
REAL m[83][174];
REAL e[83][174];
int best_score = -1;
int best_cw[174];
for (int i = 0; i < 174; i++)
for (int j = 0; j < 83; j++)
m[j][i] = codeword[i];
for (int i = 0; i < 174; i++)
for (int j = 0; j < 83; j++)
e[j][i] = 0.0;
for (int iter = 0; iter < iters; iter++)
{
for (int j = 0; j < 83; j++)
{
for (int ii1 = 0; ii1 < 7; ii1++)
{
int i1 = Arrays::Nm[j][ii1] - 1;
if (i1 < 0)
continue;
REAL a = 1.0;
for (int ii2 = 0; ii2 < 7; ii2++)
{
int i2 = Arrays::Nm[j][ii2] - 1;
if (i2 >= 0 && i2 != i1)
{
// a *= table_tanh(m[j][i2] / 2.0);
a *= fast_tanh(m[j][i2] / 2.0);
}
}
REAL tmp;
if (a >= 0.999)
{
tmp = 7.6;
}
else if (a <= -0.999)
{
tmp = -7.6;
}
else
{
tmp = log((1 + a) / (1 - a));
}
e[j][i1] = tmp;
}
}
int cw[174];
for (int i = 0; i < 174; i++)
{
REAL l = codeword[i];
for (int j = 0; j < 3; j++)
l += e[Arrays::Mn[i][j] - 1][i];
cw[i] = (l <= 0.0);
}
int score = ldpc_check(cw);
if (score == 83)
{
for (int i = 0; i < 174; i++)
plain[i] = cw[i];
*ok = 83;
return;
}
if (score > best_score)
{
for (int i = 0; i < 174; i++)
best_cw[i] = cw[i];
best_score = score;
}
for (int i = 0; i < 174; i++)
{
for (int ji1 = 0; ji1 < 3; ji1++)
{
int j1 = Arrays::Mn[i][ji1] - 1;
REAL l = codeword[i];
for (int ji2 = 0; ji2 < 3; ji2++)
{
int j2 = Arrays::Mn[i][ji2] - 1;
if (j1 != j2)
{
l += e[j2][i];
}
}
m[j1][i] = l;
}
}
}
// decode didn't work, return best guess.
for (int i = 0; i < 174; i++)
plain[i] = best_cw[i];
*ok = best_score;
}
//
// check the FT8 CRC-14
//
void LDPC::ft8_crc(int msg1[], int msglen, int out[14])
{
// the old FT8 polynomial for 12-bit CRC, 0xc06.
// int div[] = { 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0 };
// the new FT8 polynomial for 14-bit CRC, 0x2757,
// with leading 1 bit.
int div[] = {1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1};
// append 14 zeros.
int *msg = (int *)malloc(sizeof(int) * (msglen + 14));
for (int i = 0; i < msglen + 14; i++)
{
if (i < msglen)
{
msg[i] = msg1[i];
}
else
{
msg[i] = 0;
}
}
for (int i = 0; i < msglen; i++)
{
if (msg[i])
{
for (int j = 0; j < 15; j++)
{
msg[i + j] = (msg[i + j] + div[j]) % 2;
}
}
}
for (int i = 0; i < 14; i++)
{
out[i] = msg[msglen + i];
}
free(msg);
}
// rows is 91, cols is 174.
// m[174][2*91].
// m's right half should start out as zeros.
// m's upper-right quarter will be the desired inverse.
void LDPC::gauss_jordan(int rows, int cols, int m[174][2 * 91], int which[91], int *ok)
// gauss_jordan(int rows, int cols, int m[cols][2*rows], int which[rows], int *ok)
{
*ok = 0;
if ((rows != 91) || (cols != 174)) {
return;
}
for (int row = 0; row < rows; row++)
{
if (m[row][row] != 1)
{
for (int row1 = row + 1; row1 < cols; row1++)
{
if (m[row1][row] == 1)
{
// swap m[row] and m[row1]
for (int col = 0; col < 2 * rows; col++)
{
int tmp = m[row][col];
m[row][col] = m[row1][col];
m[row1][col] = tmp;
}
int tmp = which[row];
which[row] = which[row1];
which[row1] = tmp;
break;
}
}
}
if (m[row][row] != 1)
{
// could not invert
*ok = 0;
return;
}
// lazy creation of identity matrix in the upper-right quarter
m[row][rows + row] = (m[row][rows + row] + 1) % 2;
// now eliminate
for (int row1 = 0; row1 < cols; row1++)
{
if (row1 == row)
continue;
if (m[row1][row] != 0)
{
for (int col = 0; col < 2 * rows; col++)
{
m[row1][col] = (m[row1][col] + m[row][col]) % 2;
}
}
}
}
*ok = 1;
}
// # given a 174-bit codeword as an array of log-likelihood of zero,
// # return a 87-bit plain text, or zero-length array.
// # this is an implementation of the sum-product algorithm
// # from Sarah Johnson's Iterative Error Correction book.
// # codeword[i] = log ( P(x=0) / P(x=1) )
// def ldpc_decode(self, codeword):
// # 174 codeword bits
// # 87 parity checks
//
// # Mji
// # each codeword bit i tells each parity check j
// # what the bit's log-likelihood of being 0 is
// # based on information *other* than from that
// # parity check.
// m = numpy.zeros((87, 174))
//
// # Eji
// # each check j tells each codeword bit i the
// # log likelihood of the bit being zero based
// # on the *other* bits in that check.
// e = numpy.zeros((87, 174))
//
// for i in range(0, 174):
// for j in range(0, 87):
// m[j][i] = codeword[i]
//
// for iter in range(0, 50):
// # messages from checks to bits.
// # for each parity check
// for j in range(0, 87):
// # for each bit mentioned in this parity check
// for i in Nm[j]:
// if i <= 0:
// continue
// a = 1
// # for each other bit mentioned in this parity check
// for ii in Nm[j]:
// if ii != i:
// a *= math.tanh(m[j][ii-1] / 2.0)
// e[j][i-1] = math.log((1 + a) / (1 - a))
//
// # decide if we are done -- compute the corrected codeword,
// # see if the parity check succeeds.
// cw = numpy.zeros(174, dtype=numpy.int32)
// for i in range(0, 174):
// # sum the log likelihoods for codeword bit i being 0.
// l = codeword[i]
// for j in Mn[i]:
// l += e[j-1][i]
// if l > 0:
// cw[i] = 0
// else:
// cw[i] = 1
// if self.ldpc_check(cw):
// # success!
// # it's a systematic code, though the plain-text bits are scattered.
// # collect them.
// decoded = cw[colorder]
// decoded = decoded[-87:]
// return decoded
//
// # messages from bits to checks.
// for i in range(0, 174):
// for j in Mn[i]:
// l = codeword[i]
// for jj in Mn[i]:
// if jj != j:
// l += e[jj-1][i]
// m[j-1][i] = l
//
// # could not decode.
// return numpy.array([])
#if 0
static float tanhtable[] = {
-0.99990920, -0.99990737, -0.99990550, -0.99990359, -0.99990164,
-0.99989966, -0.99989763, -0.99989556, -0.99989345, -0.99989130,
-0.99988910, -0.99988686, -0.99988458, -0.99988225, -0.99987987,
-0.99987744, -0.99987496, -0.99987244, -0.99986986, -0.99986723,
-0.99986455, -0.99986182, -0.99985902, -0.99985618, -0.99985327,
-0.99985031, -0.99984728, -0.99984420, -0.99984105, -0.99983784,
-0.99983457, -0.99983122, -0.99982781, -0.99982434, -0.99982079,
-0.99981717, -0.99981348, -0.99980971, -0.99980586, -0.99980194,
-0.99979794, -0.99979386, -0.99978970, -0.99978545, -0.99978111,
-0.99977669, -0.99977218, -0.99976758, -0.99976289, -0.99975810,
-0.99975321, -0.99974823, -0.99974314, -0.99973795, -0.99973266,
-0.99972726, -0.99972175, -0.99971613, -0.99971040, -0.99970455,
-0.99969858, -0.99969249, -0.99968628, -0.99967994, -0.99967348,
-0.99966688, -0.99966016, -0.99965329, -0.99964629, -0.99963914,
-0.99963186, -0.99962442, -0.99961683, -0.99960910, -0.99960120,
-0.99959315, -0.99958493, -0.99957655, -0.99956799, -0.99955927,
-0.99955037, -0.99954129, -0.99953202, -0.99952257, -0.99951293,
-0.99950309, -0.99949305, -0.99948282, -0.99947237, -0.99946171,
-0.99945084, -0.99943975, -0.99942844, -0.99941690, -0.99940512,
-0.99939311, -0.99938085, -0.99936835, -0.99935559, -0.99934258,
-0.99932930, -0.99931576, -0.99930194, -0.99928784, -0.99927346,
-0.99925879, -0.99924382, -0.99922855, -0.99921297, -0.99919708,
-0.99918087, -0.99916432, -0.99914745, -0.99913024, -0.99911267,
-0.99909476, -0.99907648, -0.99905783, -0.99903881, -0.99901940,
-0.99899960, -0.99897940, -0.99895879, -0.99893777, -0.99891632,
-0.99889444, -0.99887212, -0.99884935, -0.99882612, -0.99880242,
-0.99877824, -0.99875358, -0.99872841, -0.99870274, -0.99867655,
-0.99864983, -0.99862258, -0.99859477, -0.99856640, -0.99853747,
-0.99850794, -0.99847782, -0.99844710, -0.99841575, -0.99838377,
-0.99835115, -0.99831787, -0.99828392, -0.99824928, -0.99821395,
-0.99817790, -0.99814112, -0.99810361, -0.99806533, -0.99802629,
-0.99798646, -0.99794582, -0.99790437, -0.99786208, -0.99781894,
-0.99777493, -0.99773003, -0.99768423, -0.99763750, -0.99758983,
-0.99754120, -0.99749159, -0.99744099, -0.99738936, -0.99733669,
-0.99728296, -0.99722815, -0.99717223, -0.99711519, -0.99705700,
-0.99699764, -0.99693708, -0.99687530, -0.99681228, -0.99674798,
-0.99668240, -0.99661549, -0.99654724, -0.99647761, -0.99640658,
-0.99633412, -0.99626020, -0.99618480, -0.99610788, -0.99602941,
-0.99594936, -0.99586770, -0.99578440, -0.99569942, -0.99561273,
-0.99552430, -0.99543409, -0.99534207, -0.99524820, -0.99515244,
-0.99505475, -0.99495511, -0.99485345, -0.99474976, -0.99464398,
-0.99453608, -0.99442601, -0.99431373, -0.99419919, -0.99408235,
-0.99396317, -0.99384159, -0.99371757, -0.99359107, -0.99346202,
-0.99333039, -0.99319611, -0.99305914, -0.99291942, -0.99277690,
-0.99263152, -0.99248323, -0.99233196, -0.99217766, -0.99202027,
-0.99185972, -0.99169596, -0.99152892, -0.99135853, -0.99118473,
-0.99100745, -0.99082663, -0.99064218, -0.99045404, -0.99026214,
-0.99006640, -0.98986674, -0.98966309, -0.98945538, -0.98924351,
-0.98902740, -0.98880698, -0.98858216, -0.98835285, -0.98811896,
-0.98788040, -0.98763708, -0.98738891, -0.98713578, -0.98687761,
-0.98661430, -0.98634574, -0.98607182, -0.98579245, -0.98550752,
-0.98521692, -0.98492053, -0.98461825, -0.98430995, -0.98399553,
-0.98367486, -0.98334781, -0.98301427, -0.98267411, -0.98232720,
-0.98197340, -0.98161259, -0.98124462, -0.98086936, -0.98048667,
-0.98009640, -0.97969840, -0.97929252, -0.97887862, -0.97845654,
-0.97802611, -0.97758719, -0.97713959, -0.97668317, -0.97621774,
-0.97574313, -0.97525917, -0.97476568, -0.97426247, -0.97374936,
-0.97322616, -0.97269268, -0.97214872, -0.97159408, -0.97102855,
-0.97045194, -0.96986402, -0.96926459, -0.96865342, -0.96803030,
-0.96739500, -0.96674729, -0.96608693, -0.96541369, -0.96472732,
-0.96402758, -0.96331422, -0.96258698, -0.96184561, -0.96108983,
-0.96031939, -0.95953401, -0.95873341, -0.95791731, -0.95708542,
-0.95623746, -0.95537312, -0.95449211, -0.95359412, -0.95267884,
-0.95174596, -0.95079514, -0.94982608, -0.94883842, -0.94783185,
-0.94680601, -0.94576057, -0.94469516, -0.94360942, -0.94250301,
-0.94137554, -0.94022664, -0.93905593, -0.93786303, -0.93664754,
-0.93540907, -0.93414721, -0.93286155, -0.93155168, -0.93021718,
-0.92885762, -0.92747257, -0.92606158, -0.92462422, -0.92316003,
-0.92166855, -0.92014933, -0.91860189, -0.91702576, -0.91542046,
-0.91378549, -0.91212037, -0.91042459, -0.90869766, -0.90693905,
-0.90514825, -0.90332474, -0.90146799, -0.89957745, -0.89765260,
-0.89569287, -0.89369773, -0.89166660, -0.88959892, -0.88749413,
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};
#endif
} // namespace FT8
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