sdrangel/ft8/libldpc.cpp

///////////////////////////////////////////////////////////////////////////////////
// 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,
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};
#endif

} // namespace FT8