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Working towards decoding, added FFT routines and a LDPC decoder

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This commit is contained in:
Karlis Goba 2018-11-07 15:50:55 +02:00
parent 0de42ee1bb
commit b8fc6e92d8
13 changed files with 1605 additions and 7 deletions
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11
Makefile
View file

@ -1,13 +1,18 @@
CXXFLAGS = -std=c++14 -I. CXXFLAGS = -std=c++14 -I.
LDFLAGS = -lm LDFLAGS = -lm
gen_ft8: gen_ft8.o ft8/encode.o ft8/pack.o ft8/text.o ft8/pack_v2.o ft8/encode_v2.o common/wave.o .PHONY: run_tests all
$(CXX) $(LDFLAGS) -o $@ $^
.PHONY: run_tests all: gen_ft8 wav_decode test
run_tests: test run_tests: test
@./test @./test
gen_ft8: gen_ft8.o ft8/encode.o ft8/pack.o ft8/text.o ft8/pack_v2.o ft8/encode_v2.o common/wave.o
$(CXX) $(LDFLAGS) -o $@ $^
test: test.o ft8/encode.o ft8/pack.o ft8/text.o ft8/pack_v2.o ft8/encode_v2.o ft8/unpack.o test: test.o ft8/encode.o ft8/pack.o ft8/text.o ft8/pack_v2.o ft8/encode_v2.o ft8/unpack.o
$(CXX) $(LDFLAGS) -o $@ $^ $(CXX) $(LDFLAGS) -o $@ $^
decode_ft8: decode_ft8.o fft/kiss_fftr.o fft/kiss_fft.o ft8/ldpc.o common/wave.o
$(CXX) $(LDFLAGS) -o $@ $^

6
README.md
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@ -25,10 +25,10 @@ I am working on the revised FT8 protocol with 77-bit payload (introduced since W
# What doesn't # What doesn't
* Encoding contest mode message * Encoding contest mode messages
* Encoding extended range signal reports (<-30dB or >=0dB S/N) * Encoding extended range signal reports (<-30dB or >=0dB S/N)
* Encoding compound callsigns with country prefixes and mode suffixes * Encoding compound callsigns with country prefixes and mode suffixes
* Decoding * Decoding (working on it)
# What to do with it # What to do with it
@ -40,5 +40,7 @@ Thanks to Robert Morris, AB1HL, whose Python code (https://github.com/rtmrtmrtmr
This would not of course be possible without the original WSJT-X code, which is mostly written in Fortran (http://physics.princeton.edu/pulsar/K1JT/wsjtx.html). I believe that is the only 'documentation' of the FT8 protocol available, and the source code was used as such in this project. This would not of course be possible without the original WSJT-X code, which is mostly written in Fortran (http://physics.princeton.edu/pulsar/K1JT/wsjtx.html). I believe that is the only 'documentation' of the FT8 protocol available, and the source code was used as such in this project.
Thanks to Mark Borgerding for his FFT implementation (https://github.com/mborgerding/kissfft). I have included a portion of his code.
Karlis Goba, Karlis Goba,
YL3JG YL3JG

64
common/wave.cpp
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@ -9,7 +9,6 @@
// Save signal in floating point format (-1 .. +1) as a WAVE file using 16-bit signed integers. // Save signal in floating point format (-1 .. +1) as a WAVE file using 16-bit signed integers.
void save_wav(const float *signal, int num_samples, int sample_rate, const char *path) { void save_wav(const float *signal, int num_samples, int sample_rate, const char *path) {
FILE *f = fopen(path, "wb");
char subChunk1ID[4] = {'f', 'm', 't', ' '}; char subChunk1ID[4] = {'f', 'm', 't', ' '};
uint32_t subChunk1Size = 16; // 16 for PCM uint32_t subChunk1Size = 16; // 16 for PCM
uint16_t audioFormat = 1; // PCM = 1 uint16_t audioFormat = 1; // PCM = 1
@ -34,6 +33,8 @@ void save_wav(const float *signal, int num_samples, int sample_rate, const char
raw_data[i] = int(0.5 + (x * 32767.0)); raw_data[i] = int(0.5 + (x * 32767.0));
} }
FILE *f = fopen(path, "wb");
// NOTE: works only on little-endian architecture // NOTE: works only on little-endian architecture
fwrite(chunkID, sizeof(chunkID), 1, f); fwrite(chunkID, sizeof(chunkID), 1, f);
fwrite(&chunkSize, sizeof(chunkSize), 1, f); fwrite(&chunkSize, sizeof(chunkSize), 1, f);
@ -57,3 +58,64 @@ void save_wav(const float *signal, int num_samples, int sample_rate, const char
free(raw_data); free(raw_data);
} }
// Load signal in floating point format (-1 .. +1) as a WAVE file using 16-bit signed integers.
int load_wav(float *signal, int &num_samples, int &sample_rate, const char *path) {
char subChunk1ID[4]; // = {'f', 'm', 't', ' '};
uint32_t subChunk1Size; // = 16; // 16 for PCM
uint16_t audioFormat; // = 1; // PCM = 1
uint16_t numChannels; // = 1;
uint16_t bitsPerSample; // = 16;
uint32_t sampleRate;
uint16_t blockAlign; // = numChannels * bitsPerSample / 8;
uint32_t byteRate; // = sampleRate * blockAlign;
char subChunk2ID[4]; // = {'d', 'a', 't', 'a'};
uint32_t subChunk2Size; // = num_samples * blockAlign;
char chunkID[4]; // = {'R', 'I', 'F', 'F'};
uint32_t chunkSize; // = 4 + (8 + subChunk1Size) + (8 + subChunk2Size);
char format[4]; // = {'W', 'A', 'V', 'E'};
FILE *f = fopen(path, "rb");
// NOTE: works only on little-endian architecture
fread((void *)chunkID, sizeof(chunkID), 1, f);
fread((void *)&chunkSize, sizeof(chunkSize), 1, f);
fread((void *)format, sizeof(format), 1, f);
fread((void *)subChunk1ID, sizeof(subChunk1ID), 1, f);
fread((void *)&subChunk1Size, sizeof(subChunk1Size), 1, f);
if (subChunk1Size != 16) return -1;
fread((void *)&audioFormat, sizeof(audioFormat), 1, f);
fread((void *)&numChannels, sizeof(numChannels), 1, f);
fread((void *)&sampleRate, sizeof(sampleRate), 1, f);
fread((void *)&byteRate, sizeof(byteRate), 1, f);
fread((void *)&blockAlign, sizeof(blockAlign), 1, f);
fread((void *)&bitsPerSample, sizeof(bitsPerSample), 1, f);
if (audioFormat != 1 || numChannels != 1 || bitsPerSample != 16) return -1;
fread((void *)subChunk2ID, sizeof(subChunk2ID), 1, f);
fread((void *)&subChunk2Size, sizeof(subChunk2Size), 1, f);
if (subChunk2Size / blockAlign > num_samples) return -2;
num_samples = subChunk2Size / blockAlign;
sample_rate = sampleRate;
int16_t *raw_data = (int16_t *)malloc(num_samples * blockAlign);
fread((void *)raw_data, blockAlign, num_samples, f);
for (int i = 0; i < num_samples; i++) {
signal[i] = raw_data[i] / 32768.0f;
}
free(raw_data);
fclose(f);
return 0;
}

2
common/wave.h
View file

@ -6,4 +6,4 @@ void save_wav(const float *signal, int num_samples, int sample_rate, const char
// Load signal in floating point format (-1 .. +1) as a WAVE file using 16-bit signed integers. // Load signal in floating point format (-1 .. +1) as a WAVE file using 16-bit signed integers.
void load_wav(float *signal, int &num_samples, int &sample_rate, const char *path); int load_wav(float *signal, int &num_samples, int &sample_rate, const char *path);

63
decode_ft8.cpp Normal file
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@ -0,0 +1,63 @@
#include <cstdlib>
#include <cstring>
#include <cstdio>
#include <cmath>
#include "common/wave.h"
#include "ft8/pack.h"
#include "ft8/encode.h"
#include "ft8/pack_v2.h"
#include "ft8/encode_v2.h"
#include "ft8/ldpc.h"
#include "fft/kiss_fftr.h"
void usage() {
printf("Decode a 15-second WAV file.\n");
}
float hann_i(int i, int N) {
float x = sinf((float)M_PI * i / (N - 1));
return x*x;
}
int main(int argc, char **argv) {
// Expect one command-line argument
if (argc < 2) {
usage();
return -1;
}
const char *wav_path = argv[1];
int sample_rate = 12000;
int num_samples = 15 * sample_rate;
float signal[num_samples];
int rc = load_wav(signal, num_samples, sample_rate, wav_path);
if (rc < 0) {
return -1;
}
//return 0;
const int nfft = 2 * (int)(sample_rate / 6.25); // 2 bins per FSK tone
size_t fft_work_size;
kiss_fftr_alloc(nfft, 0, 0, &fft_work_size);
printf("N_FFT = %d\n", nfft);
printf("FFT work area = %lu\n", fft_work_size);
void *fft_work = malloc(fft_work_size);
kiss_fftr_cfg fft_cfg = kiss_fftr_alloc(nfft, 0, fft_work, &fft_work_size);
kiss_fft_scalar timedata[nfft];
kiss_fft_cpx freqdata[nfft/2 + 1];
kiss_fftr(fft_cfg, timedata, freqdata);
return 0;
}

158
fft/_kiss_fft_guts.h Normal file
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@ -0,0 +1,158 @@
/*
* Copyright (c) 2003-2010, Mark Borgerding. All rights reserved.
* This file is part of KISS FFT - https://github.com/mborgerding/kissfft
*
* SPDX-License-Identifier: BSD-3-Clause
* See COPYING file for more information.
*/
/* kiss_fft.h
defines kiss_fft_scalar as either short or a float type
and defines
typedef struct { kiss_fft_scalar r; kiss_fft_scalar i; }kiss_fft_cpx; */
#include "kiss_fft.h"
#include <limits.h>
#define MAXFACTORS 32
/* e.g. an fft of length 128 has 4 factors
as far as kissfft is concerned
4*4*4*2
*/
struct kiss_fft_state{
int nfft;
int inverse;
int factors[2*MAXFACTORS];
kiss_fft_cpx twiddles[1];
};
/*
Explanation of macros dealing with complex math:
C_MUL(m,a,b) : m = a*b
C_FIXDIV( c , div ) : if a fixed point impl., c /= div. noop otherwise
C_SUB( res, a,b) : res = a - b
C_SUBFROM( res , a) : res -= a
C_ADDTO( res , a) : res += a
* */
#ifdef FIXED_POINT
#if (FIXED_POINT==32)
# define FRACBITS 31
# define SAMPPROD int64_t
#define SAMP_MAX 2147483647
#else
# define FRACBITS 15
# define SAMPPROD int32_t
#define SAMP_MAX 32767
#endif
#define SAMP_MIN -SAMP_MAX
#if defined(CHECK_OVERFLOW)
# define CHECK_OVERFLOW_OP(a,op,b) \
if ( (SAMPPROD)(a) op (SAMPPROD)(b) > SAMP_MAX || (SAMPPROD)(a) op (SAMPPROD)(b) < SAMP_MIN ) { \
fprintf(stderr,"WARNING:overflow @ " __FILE__ "(%d): (%d " #op" %d) = %ld\n",__LINE__,(a),(b),(SAMPPROD)(a) op (SAMPPROD)(b) ); }
#endif
# define smul(a,b) ( (SAMPPROD)(a)*(b) )
# define sround( x ) (kiss_fft_scalar)( ( (x) + (1<<(FRACBITS-1)) ) >> FRACBITS )
# define S_MUL(a,b) sround( smul(a,b) )
# define C_MUL(m,a,b) \
do{ (m).r = sround( smul((a).r,(b).r) - smul((a).i,(b).i) ); \
(m).i = sround( smul((a).r,(b).i) + smul((a).i,(b).r) ); }while(0)
# define DIVSCALAR(x,k) \
(x) = sround( smul( x, SAMP_MAX/k ) )
# define C_FIXDIV(c,div) \
do { DIVSCALAR( (c).r , div); \
DIVSCALAR( (c).i , div); }while (0)
# define C_MULBYSCALAR( c, s ) \
do{ (c).r = sround( smul( (c).r , s ) ) ;\
(c).i = sround( smul( (c).i , s ) ) ; }while(0)
#else /* not FIXED_POINT*/
# define S_MUL(a,b) ( (a)*(b) )
#define C_MUL(m,a,b) \
do{ (m).r = (a).r*(b).r - (a).i*(b).i;\
(m).i = (a).r*(b).i + (a).i*(b).r; }while(0)
# define C_FIXDIV(c,div) /* NOOP */
# define C_MULBYSCALAR( c, s ) \
do{ (c).r *= (s);\
(c).i *= (s); }while(0)
#endif
#ifndef CHECK_OVERFLOW_OP
# define CHECK_OVERFLOW_OP(a,op,b) /* noop */
#endif
#define C_ADD( res, a,b)\
do { \
CHECK_OVERFLOW_OP((a).r,+,(b).r)\
CHECK_OVERFLOW_OP((a).i,+,(b).i)\
(res).r=(a).r+(b).r; (res).i=(a).i+(b).i; \
}while(0)
#define C_SUB( res, a,b)\
do { \
CHECK_OVERFLOW_OP((a).r,-,(b).r)\
CHECK_OVERFLOW_OP((a).i,-,(b).i)\
(res).r=(a).r-(b).r; (res).i=(a).i-(b).i; \
}while(0)
#define C_ADDTO( res , a)\
do { \
CHECK_OVERFLOW_OP((res).r,+,(a).r)\
CHECK_OVERFLOW_OP((res).i,+,(a).i)\
(res).r += (a).r; (res).i += (a).i;\
}while(0)
#define C_SUBFROM( res , a)\
do {\
CHECK_OVERFLOW_OP((res).r,-,(a).r)\
CHECK_OVERFLOW_OP((res).i,-,(a).i)\
(res).r -= (a).r; (res).i -= (a).i; \
}while(0)
#ifdef FIXED_POINT
# define KISS_FFT_COS(phase) floor(.5+SAMP_MAX * cos (phase))
# define KISS_FFT_SIN(phase) floor(.5+SAMP_MAX * sin (phase))
# define HALF_OF(x) ((x)>>1)
#elif defined(USE_SIMD)
# define KISS_FFT_COS(phase) _mm_set1_ps( cos(phase) )
# define KISS_FFT_SIN(phase) _mm_set1_ps( sin(phase) )
# define HALF_OF(x) ((x)*_mm_set1_ps(.5))
#else
# define KISS_FFT_COS(phase) (kiss_fft_scalar) cos(phase)
# define KISS_FFT_SIN(phase) (kiss_fft_scalar) sin(phase)
# define HALF_OF(x) ((x)*.5)
#endif
#define kf_cexp(x,phase) \
do{ \
(x)->r = KISS_FFT_COS(phase);\
(x)->i = KISS_FFT_SIN(phase);\
}while(0)
/* a debugging function */
#define pcpx(c)\
fprintf(stderr,"%g + %gi\n",(double)((c)->r),(double)((c)->i) )
#ifdef KISS_FFT_USE_ALLOCA
// define this to allow use of alloca instead of malloc for temporary buffers
// Temporary buffers are used in two case:
// 1. FFT sizes that have "bad" factors. i.e. not 2,3 and 5
// 2. "in-place" FFTs. Notice the quotes, since kissfft does not really do an in-place transform.
#include <alloca.h>
#define KISS_FFT_TMP_ALLOC(nbytes) alloca(nbytes)
#define KISS_FFT_TMP_FREE(ptr)
#else
#define KISS_FFT_TMP_ALLOC(nbytes) KISS_FFT_MALLOC(nbytes)
#define KISS_FFT_TMP_FREE(ptr) KISS_FFT_FREE(ptr)
#endif

402
fft/kiss_fft.c Normal file
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@ -0,0 +1,402 @@
/*
* Copyright (c) 2003-2010, Mark Borgerding. All rights reserved.
* This file is part of KISS FFT - https://github.com/mborgerding/kissfft
*
* SPDX-License-Identifier: BSD-3-Clause
* See COPYING file for more information.
*/
#include "_kiss_fft_guts.h"
/* The guts header contains all the multiplication and addition macros that are defined for
fixed or floating point complex numbers. It also delares the kf_ internal functions.
*/
static void kf_bfly2(
kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st,
int m
)
{
kiss_fft_cpx * Fout2;
kiss_fft_cpx * tw1 = st->twiddles;
kiss_fft_cpx t;
Fout2 = Fout + m;
do{
C_FIXDIV(*Fout,2); C_FIXDIV(*Fout2,2);
C_MUL (t, *Fout2 , *tw1);
tw1 += fstride;
C_SUB( *Fout2 , *Fout , t );
C_ADDTO( *Fout , t );
++Fout2;
++Fout;
}while (--m);
}
static void kf_bfly4(
kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st,
const size_t m
)
{
kiss_fft_cpx *tw1,*tw2,*tw3;
kiss_fft_cpx scratch[6];
size_t k=m;
const size_t m2=2*m;
const size_t m3=3*m;
tw3 = tw2 = tw1 = st->twiddles;
do {
C_FIXDIV(*Fout,4); C_FIXDIV(Fout[m],4); C_FIXDIV(Fout[m2],4); C_FIXDIV(Fout[m3],4);
C_MUL(scratch[0],Fout[m] , *tw1 );
C_MUL(scratch[1],Fout[m2] , *tw2 );
C_MUL(scratch[2],Fout[m3] , *tw3 );
C_SUB( scratch[5] , *Fout, scratch[1] );
C_ADDTO(*Fout, scratch[1]);
C_ADD( scratch[3] , scratch[0] , scratch[2] );
C_SUB( scratch[4] , scratch[0] , scratch[2] );
C_SUB( Fout[m2], *Fout, scratch[3] );
tw1 += fstride;
tw2 += fstride*2;
tw3 += fstride*3;
C_ADDTO( *Fout , scratch[3] );
if(st->inverse) {
Fout[m].r = scratch[5].r - scratch[4].i;
Fout[m].i = scratch[5].i + scratch[4].r;
Fout[m3].r = scratch[5].r + scratch[4].i;
Fout[m3].i = scratch[5].i - scratch[4].r;
}else{
Fout[m].r = scratch[5].r + scratch[4].i;
Fout[m].i = scratch[5].i - scratch[4].r;
Fout[m3].r = scratch[5].r - scratch[4].i;
Fout[m3].i = scratch[5].i + scratch[4].r;
}
++Fout;
}while(--k);
}
static void kf_bfly3(
kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st,
size_t m
)
{
size_t k=m;
const size_t m2 = 2*m;
kiss_fft_cpx *tw1,*tw2;
kiss_fft_cpx scratch[5];
kiss_fft_cpx epi3;
epi3 = st->twiddles[fstride*m];
tw1=tw2=st->twiddles;
do{
C_FIXDIV(*Fout,3); C_FIXDIV(Fout[m],3); C_FIXDIV(Fout[m2],3);
C_MUL(scratch[1],Fout[m] , *tw1);
C_MUL(scratch[2],Fout[m2] , *tw2);
C_ADD(scratch[3],scratch[1],scratch[2]);
C_SUB(scratch[0],scratch[1],scratch[2]);
tw1 += fstride;
tw2 += fstride*2;
Fout[m].r = Fout->r - HALF_OF(scratch[3].r);
Fout[m].i = Fout->i - HALF_OF(scratch[3].i);
C_MULBYSCALAR( scratch[0] , epi3.i );
C_ADDTO(*Fout,scratch[3]);
Fout[m2].r = Fout[m].r + scratch[0].i;
Fout[m2].i = Fout[m].i - scratch[0].r;
Fout[m].r -= scratch[0].i;
Fout[m].i += scratch[0].r;
++Fout;
}while(--k);
}
static void kf_bfly5(
kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st,
int m
)
{
kiss_fft_cpx *Fout0,*Fout1,*Fout2,*Fout3,*Fout4;
int u;
kiss_fft_cpx scratch[13];
kiss_fft_cpx * twiddles = st->twiddles;
kiss_fft_cpx *tw;
kiss_fft_cpx ya,yb;
ya = twiddles[fstride*m];
yb = twiddles[fstride*2*m];
Fout0=Fout;
Fout1=Fout0+m;
Fout2=Fout0+2*m;
Fout3=Fout0+3*m;
Fout4=Fout0+4*m;
tw=st->twiddles;
for ( u=0; u<m; ++u ) {
C_FIXDIV( *Fout0,5); C_FIXDIV( *Fout1,5); C_FIXDIV( *Fout2,5); C_FIXDIV( *Fout3,5); C_FIXDIV( *Fout4,5);
scratch[0] = *Fout0;
C_MUL(scratch[1] ,*Fout1, tw[u*fstride]);
C_MUL(scratch[2] ,*Fout2, tw[2*u*fstride]);
C_MUL(scratch[3] ,*Fout3, tw[3*u*fstride]);
C_MUL(scratch[4] ,*Fout4, tw[4*u*fstride]);
C_ADD( scratch[7],scratch[1],scratch[4]);
C_SUB( scratch[10],scratch[1],scratch[4]);
C_ADD( scratch[8],scratch[2],scratch[3]);
C_SUB( scratch[9],scratch[2],scratch[3]);
Fout0->r += scratch[7].r + scratch[8].r;
Fout0->i += scratch[7].i + scratch[8].i;
scratch[5].r = scratch[0].r + S_MUL(scratch[7].r,ya.r) + S_MUL(scratch[8].r,yb.r);
scratch[5].i = scratch[0].i + S_MUL(scratch[7].i,ya.r) + S_MUL(scratch[8].i,yb.r);
scratch[6].r = S_MUL(scratch[10].i,ya.i) + S_MUL(scratch[9].i,yb.i);
scratch[6].i = -S_MUL(scratch[10].r,ya.i) - S_MUL(scratch[9].r,yb.i);
C_SUB(*Fout1,scratch[5],scratch[6]);
C_ADD(*Fout4,scratch[5],scratch[6]);
scratch[11].r = scratch[0].r + S_MUL(scratch[7].r,yb.r) + S_MUL(scratch[8].r,ya.r);
scratch[11].i = scratch[0].i + S_MUL(scratch[7].i,yb.r) + S_MUL(scratch[8].i,ya.r);
scratch[12].r = - S_MUL(scratch[10].i,yb.i) + S_MUL(scratch[9].i,ya.i);
scratch[12].i = S_MUL(scratch[10].r,yb.i) - S_MUL(scratch[9].r,ya.i);
C_ADD(*Fout2,scratch[11],scratch[12]);
C_SUB(*Fout3,scratch[11],scratch[12]);
++Fout0;++Fout1;++Fout2;++Fout3;++Fout4;
}
}
/* perform the butterfly for one stage of a mixed radix FFT */
static void kf_bfly_generic(
kiss_fft_cpx * Fout,
const size_t fstride,
const kiss_fft_cfg st,
int m,
int p
)
{
int u,k,q1,q;
kiss_fft_cpx * twiddles = st->twiddles;
kiss_fft_cpx t;
int Norig = st->nfft;
kiss_fft_cpx * scratch = (kiss_fft_cpx*)KISS_FFT_TMP_ALLOC(sizeof(kiss_fft_cpx)*p);
for ( u=0; u<m; ++u ) {
k=u;
for ( q1=0 ; q1<p ; ++q1 ) {
scratch[q1] = Fout[ k ];
C_FIXDIV(scratch[q1],p);
k += m;
}
k=u;
for ( q1=0 ; q1<p ; ++q1 ) {
int twidx=0;
Fout[ k ] = scratch[0];
for (q=1;q<p;++q ) {
twidx += fstride * k;
if (twidx>=Norig) twidx-=Norig;
C_MUL(t,scratch[q] , twiddles[twidx] );
C_ADDTO( Fout[ k ] ,t);
}
k += m;
}
}
KISS_FFT_TMP_FREE(scratch);
}
static
void kf_work(
kiss_fft_cpx * Fout,
const kiss_fft_cpx * f,
const size_t fstride,
int in_stride,
int * factors,
const kiss_fft_cfg st
)
{
kiss_fft_cpx * Fout_beg=Fout;
const int p=*factors++; /* the radix */
const int m=*factors++; /* stage's fft length/p */
const kiss_fft_cpx * Fout_end = Fout + p*m;
#ifdef _OPENMP
// use openmp extensions at the
// top-level (not recursive)
if (fstride==1 && p<=5)
{
int k;
// execute the p different work units in different threads
# pragma omp parallel for
for (k=0;k<p;++k)
kf_work( Fout +k*m, f+ fstride*in_stride*k,fstride*p,in_stride,factors,st);
// all threads have joined by this point
switch (p) {
case 2: kf_bfly2(Fout,fstride,st,m); break;
case 3: kf_bfly3(Fout,fstride,st,m); break;
case 4: kf_bfly4(Fout,fstride,st,m); break;
case 5: kf_bfly5(Fout,fstride,st,m); break;
default: kf_bfly_generic(Fout,fstride,st,m,p); break;
}
return;
}
#endif
if (m==1) {
do{
*Fout = *f;
f += fstride*in_stride;
}while(++Fout != Fout_end );
}else{
do{
// recursive call:
// DFT of size m*p performed by doing
// p instances of smaller DFTs of size m,
// each one takes a decimated version of the input
kf_work( Fout , f, fstride*p, in_stride, factors,st);
f += fstride*in_stride;
}while( (Fout += m) != Fout_end );
}
Fout=Fout_beg;
// recombine the p smaller DFTs
switch (p) {
case 2: kf_bfly2(Fout,fstride,st,m); break;
case 3: kf_bfly3(Fout,fstride,st,m); break;
case 4: kf_bfly4(Fout,fstride,st,m); break;
case 5: kf_bfly5(Fout,fstride,st,m); break;
default: kf_bfly_generic(Fout,fstride,st,m,p); break;
}
}
/* facbuf is populated by p1,m1,p2,m2, ...
where
p[i] * m[i] = m[i-1]
m0 = n */
static
void kf_factor(int n,int * facbuf)
{
int p=4;
double floor_sqrt;
floor_sqrt = floor( sqrt((double)n) );
/*factor out powers of 4, powers of 2, then any remaining primes */
do {
while (n % p) {
switch (p) {
case 4: p = 2; break;
case 2: p = 3; break;
default: p += 2; break;
}
if (p > floor_sqrt)
p = n; /* no more factors, skip to end */
}
n /= p;
*facbuf++ = p;
*facbuf++ = n;
} while (n > 1);
}
/*
*
* User-callable function to allocate all necessary storage space for the fft.
*
* The return value is a contiguous block of memory, allocated with malloc. As such,
* It can be freed with free(), rather than a kiss_fft-specific function.
* */
kiss_fft_cfg kiss_fft_alloc(int nfft,int inverse_fft,void * mem,size_t * lenmem )
{
kiss_fft_cfg st=NULL;
size_t memneeded = sizeof(struct kiss_fft_state)
+ sizeof(kiss_fft_cpx)*(nfft-1); /* twiddle factors*/
if ( lenmem==NULL ) {
st = ( kiss_fft_cfg)KISS_FFT_MALLOC( memneeded );
}else{
if (mem != NULL && *lenmem >= memneeded)
st = (kiss_fft_cfg)mem;
*lenmem = memneeded;
}
if (st) {
int i;
st->nfft=nfft;
st->inverse = inverse_fft;
for (i=0;i<nfft;++i) {
const double pi=3.141592653589793238462643383279502884197169399375105820974944;
double phase = -2*pi*i / nfft;
if (st->inverse)
phase *= -1;
kf_cexp(st->twiddles+i, phase );
}
kf_factor(nfft,st->factors);
}
return st;
}
void kiss_fft_stride(kiss_fft_cfg st,const kiss_fft_cpx *fin,kiss_fft_cpx *fout,int in_stride)
{
if (fin == fout) {
//NOTE: this is not really an in-place FFT algorithm.
//It just performs an out-of-place FFT into a temp buffer
kiss_fft_cpx * tmpbuf = (kiss_fft_cpx*)KISS_FFT_TMP_ALLOC( sizeof(kiss_fft_cpx)*st->nfft);
kf_work(tmpbuf,fin,1,in_stride, st->factors,st);
memcpy(fout,tmpbuf,sizeof(kiss_fft_cpx)*st->nfft);
KISS_FFT_TMP_FREE(tmpbuf);
}else{
kf_work( fout, fin, 1,in_stride, st->factors,st );
}
}
void kiss_fft(kiss_fft_cfg cfg,const kiss_fft_cpx *fin,kiss_fft_cpx *fout)
{
kiss_fft_stride(cfg,fin,fout,1);
}
void kiss_fft_cleanup(void)
{
// nothing needed any more
}
int kiss_fft_next_fast_size(int n)
{
while(1) {
int m=n;
while ( (m%2) == 0 ) m/=2;
while ( (m%3) == 0 ) m/=3;
while ( (m%5) == 0 ) m/=5;
if (m<=1)
break; /* n is completely factorable by twos, threes, and fives */
n++;
}
return n;
}

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/*
* Copyright (c) 2003-2010, Mark Borgerding. All rights reserved.
* This file is part of KISS FFT - https://github.com/mborgerding/kissfft
*
* SPDX-License-Identifier: BSD-3-Clause
* See COPYING file for more information.
*/
#ifndef KISS_FFT_H
#define KISS_FFT_H
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <string.h>
#ifdef __cplusplus
extern "C" {
#endif
/*
ATTENTION!
If you would like a :
-- a utility that will handle the caching of fft objects
-- real-only (no imaginary time component ) FFT
-- a multi-dimensional FFT
-- a command-line utility to perform ffts
-- a command-line utility to perform fast-convolution filtering
Then see kfc.h kiss_fftr.h kiss_fftnd.h fftutil.c kiss_fastfir.c
in the tools/ directory.
*/
#ifdef USE_SIMD
# include <xmmintrin.h>
# define kiss_fft_scalar __m128
#define KISS_FFT_MALLOC(nbytes) _mm_malloc(nbytes,16)
#define KISS_FFT_FREE _mm_free
#else
#define KISS_FFT_MALLOC malloc
#define KISS_FFT_FREE free
#endif
#ifdef FIXED_POINT
#include <sys/types.h>
# if (FIXED_POINT == 32)
# define kiss_fft_scalar int32_t
# else
# define kiss_fft_scalar int16_t
# endif
#else
# ifndef kiss_fft_scalar
/* default is float */
# define kiss_fft_scalar float
# endif
#endif
typedef struct {
kiss_fft_scalar r;
kiss_fft_scalar i;
}kiss_fft_cpx;
typedef struct kiss_fft_state* kiss_fft_cfg;
/*
* kiss_fft_alloc
*
* Initialize a FFT (or IFFT) algorithm's cfg/state buffer.
*
* typical usage: kiss_fft_cfg mycfg=kiss_fft_alloc(1024,0,NULL,NULL);
*
* The return value from fft_alloc is a cfg buffer used internally
* by the fft routine or NULL.
*
* If lenmem is NULL, then kiss_fft_alloc will allocate a cfg buffer using malloc.
* The returned value should be free()d when done to avoid memory leaks.
*
* The state can be placed in a user supplied buffer 'mem':
* If lenmem is not NULL and mem is not NULL and *lenmem is large enough,
* then the function places the cfg in mem and the size used in *lenmem
* and returns mem.
*
* If lenmem is not NULL and ( mem is NULL or *lenmem is not large enough),
* then the function returns NULL and places the minimum cfg
* buffer size in *lenmem.
* */
kiss_fft_cfg kiss_fft_alloc(int nfft,int inverse_fft,void * mem,size_t * lenmem);
/*
* kiss_fft(cfg,in_out_buf)
*
* Perform an FFT on a complex input buffer.
* for a forward FFT,
* fin should be f[0] , f[1] , ... ,f[nfft-1]
* fout will be F[0] , F[1] , ... ,F[nfft-1]
* Note that each element is complex and can be accessed like
f[k].r and f[k].i
* */
void kiss_fft(kiss_fft_cfg cfg,const kiss_fft_cpx *fin,kiss_fft_cpx *fout);
/*
A more generic version of the above function. It reads its input from every Nth sample.
* */
void kiss_fft_stride(kiss_fft_cfg cfg,const kiss_fft_cpx *fin,kiss_fft_cpx *fout,int fin_stride);
/* If kiss_fft_alloc allocated a buffer, it is one contiguous
buffer and can be simply free()d when no longer needed*/
#define kiss_fft_free KISS_FFT_FREE
/*
Cleans up some memory that gets managed internally. Not necessary to call, but it might clean up
your compiler output to call this before you exit.
*/
void kiss_fft_cleanup(void);
/*
* Returns the smallest integer k, such that k>=n and k has only "fast" factors (2,3,5)
*/
int kiss_fft_next_fast_size(int n);
/* for real ffts, we need an even size */
#define kiss_fftr_next_fast_size_real(n) \
(kiss_fft_next_fast_size( ((n)+1)>>1)<<1)
#ifdef __cplusplus
}
#endif
#endif

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/*
* Copyright (c) 2003-2004, Mark Borgerding. All rights reserved.
* This file is part of KISS FFT - https://github.com/mborgerding/kissfft
*
* SPDX-License-Identifier: BSD-3-Clause
* See COPYING file for more information.
*/
#include "kiss_fftr.h"
#include "_kiss_fft_guts.h"
struct kiss_fftr_state{
kiss_fft_cfg substate;
kiss_fft_cpx * tmpbuf;
kiss_fft_cpx * super_twiddles;
#ifdef USE_SIMD
void * pad;
#endif
};
kiss_fftr_cfg kiss_fftr_alloc(int nfft,int inverse_fft,void * mem,size_t * lenmem)
{
int i;
kiss_fftr_cfg st = NULL;
size_t subsize = 0, memneeded;
if (nfft & 1) {
fprintf(stderr,"Real FFT optimization must be even.\n");
return NULL;
}
nfft >>= 1;
kiss_fft_alloc (nfft, inverse_fft, NULL, &subsize);
memneeded = sizeof(struct kiss_fftr_state) + subsize + sizeof(kiss_fft_cpx) * ( nfft * 3 / 2);
if (lenmem == NULL) {
st = (kiss_fftr_cfg) KISS_FFT_MALLOC (memneeded);
} else {
if (*lenmem >= memneeded)
st = (kiss_fftr_cfg) mem;
*lenmem = memneeded;
}
if (!st)
return NULL;
st->substate = (kiss_fft_cfg) (st + 1); /*just beyond kiss_fftr_state struct */
st->tmpbuf = (kiss_fft_cpx *) (((char *) st->substate) + subsize);
st->super_twiddles = st->tmpbuf + nfft;
kiss_fft_alloc(nfft, inverse_fft, st->substate, &subsize);
for (i = 0; i < nfft/2; ++i) {
double phase =
-3.14159265358979323846264338327 * ((double) (i+1) / nfft + .5);
if (inverse_fft)
phase *= -1;
kf_cexp (st->super_twiddles+i,phase);
}
return st;
}
void kiss_fftr(kiss_fftr_cfg st,const kiss_fft_scalar *timedata,kiss_fft_cpx *freqdata)
{
/* input buffer timedata is stored row-wise */
int k,ncfft;
kiss_fft_cpx fpnk,fpk,f1k,f2k,tw,tdc;
if ( st->substate->inverse) {
fprintf(stderr,"kiss fft usage error: improper alloc\n");
exit(1);
}
ncfft = st->substate->nfft;
/*perform the parallel fft of two real signals packed in real,imag*/
kiss_fft( st->substate , (const kiss_fft_cpx*)timedata, st->tmpbuf );
/* The real part of the DC element of the frequency spectrum in st->tmpbuf
* contains the sum of the even-numbered elements of the input time sequence
* The imag part is the sum of the odd-numbered elements
*
* The sum of tdc.r and tdc.i is the sum of the input time sequence.
* yielding DC of input time sequence
* The difference of tdc.r - tdc.i is the sum of the input (dot product) [1,-1,1,-1...
* yielding Nyquist bin of input time sequence
*/
tdc.r = st->tmpbuf[0].r;
tdc.i = st->tmpbuf[0].i;
C_FIXDIV(tdc,2);
CHECK_OVERFLOW_OP(tdc.r ,+, tdc.i);
CHECK_OVERFLOW_OP(tdc.r ,-, tdc.i);
freqdata[0].r = tdc.r + tdc.i;
freqdata[ncfft].r = tdc.r - tdc.i;
#ifdef USE_SIMD
freqdata[ncfft].i = freqdata[0].i = _mm_set1_ps(0);
#else
freqdata[ncfft].i = freqdata[0].i = 0;
#endif
for ( k=1;k <= ncfft/2 ; ++k ) {
fpk = st->tmpbuf[k];
fpnk.r = st->tmpbuf[ncfft-k].r;
fpnk.i = - st->tmpbuf[ncfft-k].i;
C_FIXDIV(fpk,2);
C_FIXDIV(fpnk,2);
C_ADD( f1k, fpk , fpnk );
C_SUB( f2k, fpk , fpnk );
C_MUL( tw , f2k , st->super_twiddles[k-1]);
freqdata[k].r = HALF_OF(f1k.r + tw.r);
freqdata[k].i = HALF_OF(f1k.i + tw.i);
freqdata[ncfft-k].r = HALF_OF(f1k.r - tw.r);
freqdata[ncfft-k].i = HALF_OF(tw.i - f1k.i);
}
}
void kiss_fftri(kiss_fftr_cfg st,const kiss_fft_cpx *freqdata,kiss_fft_scalar *timedata)
{
/* input buffer timedata is stored row-wise */
int k, ncfft;
if (st->substate->inverse == 0) {
fprintf (stderr, "kiss fft usage error: improper alloc\n");
exit (1);
}
ncfft = st->substate->nfft;
st->tmpbuf[0].r = freqdata[0].r + freqdata[ncfft].r;
st->tmpbuf[0].i = freqdata[0].r - freqdata[ncfft].r;
C_FIXDIV(st->tmpbuf[0],2);
for (k = 1; k <= ncfft / 2; ++k) {
kiss_fft_cpx fk, fnkc, fek, fok, tmp;
fk = freqdata[k];
fnkc.r = freqdata[ncfft - k].r;
fnkc.i = -freqdata[ncfft - k].i;
C_FIXDIV( fk , 2 );
C_FIXDIV( fnkc , 2 );
C_ADD (fek, fk, fnkc);
C_SUB (tmp, fk, fnkc);
C_MUL (fok, tmp, st->super_twiddles[k-1]);
C_ADD (st->tmpbuf[k], fek, fok);
C_SUB (st->tmpbuf[ncfft - k], fek, fok);
#ifdef USE_SIMD
st->tmpbuf[ncfft - k].i *= _mm_set1_ps(-1.0);
#else
st->tmpbuf[ncfft - k].i *= -1;
#endif
}
kiss_fft (st->substate, st->tmpbuf, (kiss_fft_cpx *) timedata);
}

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/*
* Copyright (c) 2003-2004, Mark Borgerding. All rights reserved.
* This file is part of KISS FFT - https://github.com/mborgerding/kissfft
*
* SPDX-License-Identifier: BSD-3-Clause
* See COPYING file for more information.
*/
#ifndef KISS_FTR_H
#define KISS_FTR_H
#include "kiss_fft.h"
#ifdef __cplusplus
extern "C" {
#endif
/*
Real optimized version can save about 45% cpu time vs. complex fft of a real seq.
*/
typedef struct kiss_fftr_state *kiss_fftr_cfg;
kiss_fftr_cfg kiss_fftr_alloc(int nfft,int inverse_fft,void * mem, size_t * lenmem);
/*
nfft must be even
If you don't care to allocate space, use mem = lenmem = NULL
*/
void kiss_fftr(kiss_fftr_cfg cfg,const kiss_fft_scalar *timedata,kiss_fft_cpx *freqdata);
/*
input timedata has nfft scalar points
output freqdata has nfft/2+1 complex points
*/
void kiss_fftri(kiss_fftr_cfg cfg,const kiss_fft_cpx *freqdata,kiss_fft_scalar *timedata);
/*
input freqdata has nfft/2+1 complex points
output timedata has nfft scalar points
*/
#define kiss_fftr_free KISS_FFT_FREE
#ifdef __cplusplus
}
#endif
#endif

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// LDPC(174,87) parameters from WSJT-X.
// this is an indirection table that moves a
// codeword's 87 systematic (message) bits to the end.
int colorder[] = {
0, 1, 2, 3, 30, 4, 5, 6, 7, 8, 9, 10, 11, 32, 12, 40, 13, 14, 15, 16,
17, 18, 37, 45, 29, 19, 20, 21, 41, 22, 42, 31, 33, 34, 44, 35, 47,
51, 50, 43, 36, 52, 63, 46, 25, 55, 27, 24, 23, 53, 39, 49, 59, 38,
48, 61, 60, 57, 28, 62, 56, 58, 65, 66, 26, 70, 64, 69, 68, 67, 74,
71, 54, 76, 72, 75, 78, 77, 80, 79, 73, 83, 84, 81, 82, 85, 86, 87,
88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103,
104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117,
118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131,
132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145,
146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159,
160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173
};
// this is the LDPC(174,87) parity check matrix.
// 87 rows.
// each row describes one parity check.
// each number is an index into the codeword (1-origin).
// the codeword bits mentioned in each row must xor to zero.
// From WSJT-X's bpdecode174.f90.
int Nm[][7] = {
{1, 30, 60, 89, 118, 147, 0},
{2, 31, 61, 90, 119, 147, 0},
{3, 32, 62, 91, 120, 148, 0},
{4, 33, 63, 92, 121, 149, 0},
{2, 34, 64, 93, 122, 150, 0},
{5, 33, 65, 94, 123, 148, 0},
{6, 34, 66, 95, 124, 151, 0},
{7, 35, 67, 96, 120, 152, 0},
{8, 36, 68, 97, 125, 153, 0},
{9, 37, 69, 98, 126, 152, 0},
{10, 38, 70, 99, 127, 154, 0},
{11, 39, 71, 100, 126, 155, 0},
{12, 40, 61, 101, 128, 145, 0},
{10, 33, 60, 95, 128, 156, 0},
{13, 41, 72, 97, 126, 157, 0},
{13, 42, 73, 90, 129, 156, 0},
{14, 39, 74, 99, 130, 158, 0},
{15, 43, 75, 102, 131, 159, 0},
{16, 43, 71, 103, 118, 160, 0},
{17, 44, 76, 98, 130, 156, 0},
{18, 45, 60, 96, 132, 161, 0},
{19, 46, 73, 83, 133, 162, 0},
{12, 38, 77, 102, 134, 163, 0},
{19, 47, 78, 104, 135, 147, 0},
{1, 32, 77, 105, 136, 164, 0},
{20, 48, 73, 106, 123, 163, 0},
{21, 41, 79, 107, 137, 165, 0},
{22, 42, 66, 108, 138, 152, 0},
{18, 42, 80, 109, 139, 154, 0},
{23, 49, 81, 110, 135, 166, 0},
{16, 50, 82, 91, 129, 158, 0},
{3, 48, 63, 107, 124, 167, 0},
{6, 51, 67, 111, 134, 155, 0},
{24, 35, 77, 100, 122, 162, 0},
{20, 45, 76, 112, 140, 157, 0},
{21, 36, 64, 92, 130, 159, 0},
{8, 52, 83, 111, 118, 166, 0},
{21, 53, 84, 113, 138, 168, 0},
{25, 51, 79, 89, 122, 158, 0},
{22, 44, 75, 107, 133, 155, 172},
{9, 54, 84, 90, 141, 169, 0},
{22, 54, 85, 110, 136, 161, 0},
{8, 37, 65, 102, 129, 170, 0},
{19, 39, 85, 114, 139, 150, 0},
{26, 55, 71, 93, 142, 167, 0},
{27, 56, 65, 96, 133, 160, 174},
{28, 31, 86, 100, 117, 171, 0},
{28, 52, 70, 104, 132, 144, 0},
{24, 57, 68, 95, 137, 142, 0},
{7, 30, 72, 110, 143, 151, 0},
{4, 51, 76, 115, 127, 168, 0},
{16, 45, 87, 114, 125, 172, 0},
{15, 30, 86, 115, 123, 150, 0},
{23, 46, 64, 91, 144, 173, 0},
{23, 35, 75, 113, 145, 153, 0},
{14, 41, 87, 108, 117, 149, 170},
{25, 40, 85, 94, 124, 159, 0},
{25, 58, 69, 116, 143, 174, 0},
{29, 43, 61, 116, 132, 162, 0},
{15, 58, 88, 112, 121, 164, 0},
{4, 59, 72, 114, 119, 163, 173},
{27, 47, 86, 98, 134, 153, 0},
{5, 44, 78, 109, 141, 0, 0},
{10, 46, 69, 103, 136, 165, 0},
{9, 50, 59, 93, 128, 164, 0},
{14, 57, 58, 109, 120, 166, 0},
{17, 55, 62, 116, 125, 154, 0},
{3, 54, 70, 101, 140, 170, 0},
{1, 36, 82, 108, 127, 174, 0},
{5, 53, 81, 105, 140, 0, 0},
{29, 53, 67, 99, 142, 173, 0},
{18, 49, 74, 97, 115, 167, 0},
{2, 57, 63, 103, 138, 157, 0},
{26, 38, 79, 112, 135, 171, 0},
{11, 52, 66, 88, 119, 148, 0},
{20, 40, 68, 117, 141, 160, 0},
{11, 48, 81, 89, 146, 169, 0},
{29, 47, 80, 92, 146, 172, 0},
{6, 32, 87, 104, 145, 169, 0},
{27, 34, 74, 106, 131, 165, 0},
{12, 56, 84, 88, 139, 0, 0},
{13, 56, 62, 111, 146, 171, 0},
{26, 37, 80, 105, 144, 151, 0},
{17, 31, 82, 113, 121, 161, 0},
{28, 49, 59, 94, 137, 0, 0},
{7, 55, 83, 101, 131, 168, 0},
{24, 50, 78, 106, 143, 149, 0},
};
// Mn from WSJT-X's bpdecode174.f90.
// each row corresponds to a codeword bit.
// the numbers indicate which three parity
// checks (rows in Nm) refer to the codeword bit.
// 1-origin.
int Mn[][3] = {
{1, 25, 69},
{2, 5, 73},
{3, 32, 68},
{4, 51, 61},
{6, 63, 70},
{7, 33, 79},
{8, 50, 86},
{9, 37, 43},
{10, 41, 65},
{11, 14, 64},
{12, 75, 77},
{13, 23, 81},
{15, 16, 82},
{17, 56, 66},
{18, 53, 60},
{19, 31, 52},
{20, 67, 84},
{21, 29, 72},
{22, 24, 44},
{26, 35, 76},
{27, 36, 38},
{28, 40, 42},
{30, 54, 55},
{34, 49, 87},
{39, 57, 58},
{45, 74, 83},
{46, 62, 80},
{47, 48, 85},
{59, 71, 78},
{1, 50, 53},
{2, 47, 84},
{3, 25, 79},
{4, 6, 14},
{5, 7, 80},
{8, 34, 55},
{9, 36, 69},
{10, 43, 83},
{11, 23, 74},
{12, 17, 44},
{13, 57, 76},
{15, 27, 56},
{16, 28, 29},
{18, 19, 59},
{20, 40, 63},
{21, 35, 52},
{22, 54, 64},
{24, 62, 78},
{26, 32, 77},
{30, 72, 85},
{31, 65, 87},
{33, 39, 51},
{37, 48, 75},
{38, 70, 71},
{41, 42, 68},
{45, 67, 86},
{46, 81, 82},
{49, 66, 73},
{58, 60, 66},
{61, 65, 85},
{1, 14, 21},
{2, 13, 59},
{3, 67, 82},
{4, 32, 73},
{5, 36, 54},
{6, 43, 46},
{7, 28, 75},
{8, 33, 71},
{9, 49, 76},
{10, 58, 64},
{11, 48, 68},
{12, 19, 45},
{15, 50, 61},
{16, 22, 26},
{17, 72, 80},
{18, 40, 55},
{20, 35, 51},
{23, 25, 34},
{24, 63, 87},
{27, 39, 74},
{29, 78, 83},
{30, 70, 77},
{31, 69, 84},
{22, 37, 86},
{38, 41, 81},
{42, 44, 57},
{47, 53, 62},
{52, 56, 79},
{60, 75, 81},
{1, 39, 77},
{2, 16, 41},
{3, 31, 54},
{4, 36, 78},
{5, 45, 65},
{6, 57, 85},
{7, 14, 49},
{8, 21, 46},
{9, 15, 72},
{10, 20, 62},
{11, 17, 71},
{12, 34, 47},
{13, 68, 86},
{18, 23, 43},
{19, 64, 73},
{24, 48, 79},
{25, 70, 83},
{26, 80, 87},
{27, 32, 40},
{28, 56, 69},
{29, 63, 66},
{30, 42, 50},
{33, 37, 82},
{35, 60, 74},
{38, 55, 84},
{44, 52, 61},
{51, 53, 72},
{58, 59, 67},
{47, 56, 76},
{1, 19, 37},
{2, 61, 75},
{3, 8, 66},
{4, 60, 84},
{5, 34, 39},
{6, 26, 53},
{7, 32, 57},
{9, 52, 67},
{10, 12, 15},
{11, 51, 69},
{13, 14, 65},
{16, 31, 43},
{17, 20, 36},
{18, 80, 86},
{21, 48, 59},
{22, 40, 46},
{23, 33, 62},
{24, 30, 74},
{25, 42, 64},
{27, 49, 85},
{28, 38, 73},
{29, 44, 81},
{35, 68, 70},
{41, 63, 76},
{45, 49, 71},
{50, 58, 87},
{48, 54, 83},
{13, 55, 79},
{77, 78, 82},
{1, 2, 24},
{3, 6, 75},
{4, 56, 87},
{5, 44, 53},
{7, 50, 83},
{8, 10, 28},
{9, 55, 62},
{11, 29, 67},
{12, 33, 40},
{14, 16, 20},
{15, 35, 73},
{17, 31, 39},
{18, 36, 57},
{19, 46, 76},
{21, 42, 84},
{22, 34, 59},
{23, 26, 61},
{25, 60, 65},
{27, 64, 80},
{30, 37, 66},
{32, 45, 72},
{38, 51, 86},
{41, 77, 79},
{43, 56, 68},
{47, 74, 82},
{40, 52, 78},
{54, 61, 71},
{46, 58, 69},
};

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ft8/ldpc.cpp Normal file
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//
// LDPC decoder for FT8.
//
// given a 174-bit codeword as an array of log-likelihood of zero,
// return a 174-bit corrected codeword, or zero-length array.
// last 87 bits are the (systematic) plain-text.
// 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) )
//
// cc -O3 libldpc.c -shared -fPIC -o libldpc.so
//
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include "arrays.h"
int ldpc_check(int codeword[]);
// thank you Douglas Bagnall
// https://math.stackexchange.com/a/446411
float fast_tanh(float x)
{
if (x < -4.97f)
{
return -1.0f;
}
if (x > 4.97f)
{
return 1.0f;
}
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;
}
// codeword is 174 log-likelihoods.
// plain is a return value, 174 ints, to be 0 or 1.
// iters is how hard to try.
// ok == 87 means success.
void ldpc_decode(float codeword[], int iters, int plain[], int *ok)
{
float m[87][174]; // ~60 kB
float e[87][174]; // ~60 kB
int best_score = -1;
int best_cw[174];
for (int i = 0; i < 174; i++)
for (int j = 0; j < 87; j++)
m[j][i] = codeword[i];
for (int i = 0; i < 174; i++)
for (int j = 0; j < 87; j++)
e[j][i] = 0.0f;
for (int iter = 0; iter < iters; iter++)
{
for (int j = 0; j < 87; j++)
{
for (int ii1 = 0; ii1 < 7; ii1++)
{
int i1 = Nm[j][ii1] - 1;
if (i1 < 0)
continue;
float a = 1.0f;
for (int ii2 = 0; ii2 < 7; ii2++)
{
int i2 = Nm[j][ii2] - 1;
if (i2 >= 0 && i2 != i1)
{
a *= fast_tanh(m[j][i2] / 2.0f);
}
}
e[j][i1] = log((1 + a) / (1 - a));
}
}
int cw[174];
for (int i = 0; i < 174; i++)
{
float l = codeword[i];
for (int j = 0; j < 3; j++)
l += e[Mn[i][j] - 1][i];
cw[i] = (l <= 0.0f);
}
int score = ldpc_check(cw);
if (score == 87)
{
// Found a perfect answer
#if 0
int cw1[174];
for(int i = 0; i < 174; i++)
cw1[i] = cw[colorder[i]];
for(int i = 0; i < 87; i++)
plain[i] = cw1[174-87+i];
#else
for (int i = 0; i < 174; i++)
plain[i] = cw[colorder[i]];
#endif
*ok = 87;
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 = Mn[i][ji1] - 1;
float l = codeword[i];
for (int ji2 = 0; ji2 < 3; ji2++)
{
if (ji1 != ji2)
{
int j2 = Mn[i][ji2] - 1;
l += e[j2][i];
}
}
m[j1][i] = l;
}
}
}
// decode didn't work, return something anyway.
#if 0
int cw1[174];
for(int i = 0; i < 174; i++)
cw1[i] = best_cw[colorder[i]];
for(int i = 0; i < 87; i++)
plain[i] = cw1[174-87+i];
#else
for (int i = 0; i < 174; i++)
plain[i] = best_cw[colorder[i]];
#endif
*ok = best_score;
}
//
// does a 174-bit codeword pass the FT8's LDPC parity checks?
// returns the number of parity checks that passed.
// 87 means total success.
//
int ldpc_check(int codeword[])
{
int score = 0;
// Nm[87][7]
for (int j = 0; j < 87; j++)
{
int x = 0;
for (int ii1 = 0; ii1 < 7; ii1++)
{
int i1 = Nm[j][ii1] - 1;
if (i1 >= 0)
{
x ^= codeword[i1];
}
}
if (x == 0)
score++;
}
return score;
}
/*
def bp_decode(codeword, max_iterations = 10):
## 174 codeword bits
## 87 parity checks
mnx = numpy.array(Mn, dtype=numpy.int32)
nmx = numpy.array(Nm, dtype=numpy.int32)
ncw = 3
tov = numpy.zeros( (3, N) )
toc = numpy.zeros( (7, M) )
tanhtoc = numpy.zeros( (7, M) )
zn = numpy.zeros(N)
nclast = 0
ncnt = 0
# initialize messages to checks
for j in range(M):
for i in range(nrw[j]):
toc[i, j] = codeword[nmx[j, i] - 1]
for iteration in range(max_iterations):
# Update bit log likelihood ratios (tov=0 in iteration 0).
#for i in range(N):
# zn[i] = codeword[i] + numpy.sum(tov[:,i])
zn = codeword + numpy.sum(tov, axis = 0)
#print(numpy.sum(tov, axis=0))
# Check to see if we have a codeword (check before we do any iteration).
cw = numpy.zeros(N, dtype=numpy.int32)
cw[zn > 0] = 1
ncheck = 0
for i in range(M):
synd = numpy.sum(cw[ nmx[i, :nrw[i]]-1 ])
if synd % 2 > 0:
ncheck += 1
if ncheck == 0:
# we have a codeword - reorder the columns and return it
codeword = cw[colorder]
#nerr = 0
#for i in range(N):
# if (2*cw[i]-1)*codeword[i] < 0:
# nerr += 1
#print("DECODED!", nerr)
return codeword[M:N]
if iter > 0:
# this code block implements an early stopping criterion
nd = ncheck - nclast
if nd < 0: # of unsatisfied parity checks decreased
ncnt = 0 # reset counter
else:
ncnt += 1
if ncnt >= 5 and iter >= 10 and ncheck >= 15:
nharderror = -1
#return numpy.array([])
nclast = ncheck
# Send messages from bits to check nodes
for j in range(M):
for i in range(nrw[j]):
ibj = nmx[j, i] - 1
toc[i, j] = zn[ibj]
for kk in range(ncw): # subtract off what the bit had received from the check
if mnx[ibj, kk] - 1 == j:
toc[i, j] -= tov[kk, ibj]
# send messages from check nodes to variable nodes
#for i in range(M):
# tanhtoc[:,i] = numpy.tanh(-toc[:,i] / 2)
tanhtoc = numpy.tanh(-toc / 2)
for j in range(N):
for i in range(ncw):
ichk = mnx[j, i] - 1 # Mn(:,j) are the checks that include bit j
Tmn = 1.0
for k in range(nrw[ichk]):
if nmx[ichk, k] - 1 == j: continue
Tmn *= tanhtoc[k, ichk]
y = numpy.arctanh(-Tmn)
#y = platanh(-Tmn)
tov[i, j] = 2*y
return numpy.array([])
*/

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#pragma once
// codeword is 174 log-likelihoods.
// plain is a return value, 174 ints, to be 0 or 1.
// iters is how hard to try.
// ok == 87 means success.
void ldpc_decode(float codeword[], int iters, int plain[], int *ok);