332 lines
No EOL
8.8 KiB
C++
332 lines
No EOL
8.8 KiB
C++
//
|
|
// 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) )
|
|
//
|
|
#include "ldpc.h"
|
|
|
|
#include <stdio.h>
|
|
#include <math.h>
|
|
#include <stdlib.h>
|
|
|
|
namespace ft8 {
|
|
|
|
static int ldpc_check(uint8_t codeword[]);
|
|
static float fast_tanh(float x);
|
|
static float fast_atanh(float x);
|
|
|
|
|
|
// Packs a string of bits each represented as a zero/non-zero byte in plain[],
|
|
// as a string of packed bits starting from the MSB of the first byte of packed[]
|
|
void pack_bits(const uint8_t plain[], int num_bits, uint8_t packed[]) {
|
|
int num_bytes = (num_bits + 7) / 8;
|
|
for (int i = 0; i < num_bytes; ++i) {
|
|
packed[i] = 0;
|
|
}
|
|
|
|
uint8_t mask = 0x80;
|
|
int byte_idx = 0;
|
|
for (int i = 0; i < num_bits; ++i) {
|
|
if (plain[i]) {
|
|
packed[byte_idx] |= mask;
|
|
}
|
|
mask >>= 1;
|
|
if (!mask) {
|
|
mask = 0x80;
|
|
++byte_idx;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// codeword is 174 log-likelihoods.
|
|
// plain is a return value, 174 ints, to be 0 or 1.
|
|
// max_iters is how hard to try.
|
|
// n_errors == 87 means success.
|
|
void ldpc_decode(const float codeword[], int max_iters, uint8_t plain[], int *n_errors) {
|
|
float m[ft8::M][ft8::N]; // ~60 kB
|
|
float e[ft8::M][ft8::N]; // ~60 kB
|
|
int min_errors = ft8::M;
|
|
int n_err_last = 0;
|
|
int n_cnt = 0;
|
|
|
|
for (int j = 0; j < ft8::M; j++) {
|
|
for (int i = 0; i < ft8::N; i++) {
|
|
m[j][i] = codeword[i];
|
|
e[j][i] = 0.0f;
|
|
}
|
|
}
|
|
|
|
for (int iter = 0; iter < max_iters; iter++) {
|
|
for (int j = 0; j < ft8::M; j++) {
|
|
for (int ii1 = 0; ii1 < kNrw[j]; ii1++) {
|
|
int i1 = kNm[j][ii1] - 1;
|
|
float a = 1.0f;
|
|
for (int ii2 = 0; ii2 < kNrw[j]; ii2++) {
|
|
int i2 = kNm[j][ii2] - 1;
|
|
if (i2 != i1) {
|
|
a *= fast_tanh(-m[j][i2] / 2.0f);
|
|
}
|
|
}
|
|
e[j][i1] = logf((1 - a) / (1 + a));
|
|
}
|
|
}
|
|
|
|
for (int i = 0; i < ft8::N; i++) {
|
|
float l = codeword[i];
|
|
for (int j = 0; j < 3; j++)
|
|
l += e[kMn[i][j] - 1][i];
|
|
plain[i] = (l > 0) ? 1 : 0;
|
|
}
|
|
|
|
int errors = ldpc_check(plain);
|
|
|
|
if (errors < min_errors) {
|
|
// Update the current best result
|
|
min_errors = errors;
|
|
|
|
if (errors == 0) {
|
|
break; // Found a perfect answer
|
|
}
|
|
}
|
|
|
|
// Early stopping criterion
|
|
if (iter > 0) {
|
|
int nd = errors - n_err_last;
|
|
if (nd < 0) {
|
|
n_cnt = 0;
|
|
}
|
|
else {
|
|
++n_cnt;
|
|
}
|
|
if (n_cnt >= 5 && iter >= 10 && errors >= 15) {
|
|
*n_errors = errors;
|
|
return;
|
|
}
|
|
}
|
|
n_err_last = errors;
|
|
|
|
for (int i = 0; i < ft8::N; i++) {
|
|
for (int ji1 = 0; ji1 < 3; ji1++) {
|
|
int j1 = kMn[i][ji1] - 1;
|
|
float l = codeword[i];
|
|
for (int ji2 = 0; ji2 < 3; ji2++) {
|
|
if (ji1 != ji2) {
|
|
int j2 = kMn[i][ji2] - 1;
|
|
l += e[j2][i];
|
|
}
|
|
}
|
|
m[j1][i] = l;
|
|
}
|
|
}
|
|
}
|
|
|
|
*n_errors = min_errors;
|
|
}
|
|
|
|
|
|
//
|
|
// does a 174-bit codeword pass the FT8's LDPC parity checks?
|
|
// returns the number of parity errors.
|
|
// 0 means total success.
|
|
//
|
|
static int ldpc_check(uint8_t codeword[]) {
|
|
int errors = 0;
|
|
|
|
for (int j = 0; j < ft8::M; ++j) {
|
|
uint8_t x = 0;
|
|
for (int i = 0; i < kNrw[j]; ++i) {
|
|
x ^= codeword[kNm[j][i] - 1];
|
|
}
|
|
if (x != 0) {
|
|
++errors;
|
|
}
|
|
}
|
|
return errors;
|
|
}
|
|
|
|
|
|
void BPDecoderState::reset() {
|
|
// initialize messages to checks
|
|
for (int i = 0; i < ft8::N; ++i) {
|
|
for (int j = 0; j < 3; ++j) {
|
|
tov[i][j] = 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
int BPDecoderState::iterate(const float codeword[], uint8_t plain[]) {
|
|
// Update bit log likelihood ratios (tov=0 in iter 0)
|
|
float zn[ft8::N];
|
|
for (int i = 0; i < ft8::N; ++i) {
|
|
zn[i] = codeword[i] + tov[i][0] + tov[i][1] + tov[i][2];
|
|
plain[i] = (zn[i] > 0) ? 1 : 0;
|
|
}
|
|
|
|
// Check to see if we have a codeword (check before we do any iter)
|
|
int errors = ldpc_check(plain);
|
|
|
|
if (errors == 0) {
|
|
return 0; // Found a perfect answer
|
|
}
|
|
|
|
// Send messages from bits to check nodes
|
|
for (int i = 0; i < ft8::M; ++i) {
|
|
for (int j = 0; j < kNrw[i]; ++j) {
|
|
int ibj = kNm[i][j] - 1;
|
|
toc[i][j] = zn[ibj];
|
|
for (int kk = 0; kk < 3; ++kk) {
|
|
// subtract off what the bit had received from the check
|
|
if (kMn[ibj][kk] - 1 == i) {
|
|
toc[i][j] -= tov[ibj][kk];
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// send messages from check nodes to variable nodes
|
|
for (int i = 0; i < ft8::M; ++i) {
|
|
for (int j = 0; j < kNrw[i]; ++j) {
|
|
toc[i][j] = fast_tanh(-toc[i][j] / 2);
|
|
}
|
|
}
|
|
|
|
for (int i = 0; i < ft8::N; ++i) {
|
|
for (int j = 0; j < 3; ++j) {
|
|
int ichk = kMn[i][j] - 1; // kMn(:,j) are the checks that include bit j
|
|
float Tmn = 1.0f;
|
|
for (int k = 0; k < kNrw[ichk]; ++k) {
|
|
if (kNm[ichk][k] - 1 != i) {
|
|
Tmn *= toc[ichk][k];
|
|
}
|
|
}
|
|
tov[i][j] = 2 * fast_atanh(-Tmn);
|
|
}
|
|
}
|
|
|
|
return errors;
|
|
}
|
|
|
|
|
|
|
|
void bp_decode(const float codeword[], int max_iters, uint8_t plain[], int *n_errors) {
|
|
BPDecoderState state;
|
|
|
|
int n_err_last = 0;
|
|
int n_cnt = 0;
|
|
|
|
state.reset();
|
|
*n_errors = ft8::M;
|
|
|
|
for (int iter = 0; iter < max_iters; ++iter) {
|
|
int errors = state.iterate(codeword, plain);
|
|
if (errors < *n_errors) {
|
|
*n_errors = errors;
|
|
}
|
|
if (errors == 0) return;
|
|
|
|
// Early stopping criterion
|
|
if (iter > 0) {
|
|
int nd = errors - n_err_last;
|
|
if (nd < 0) {
|
|
n_cnt = 0;
|
|
}
|
|
else {
|
|
++n_cnt;
|
|
}
|
|
if (n_cnt >= 5 && iter >= 10 && errors >= 15) {
|
|
*n_errors = errors;
|
|
return;
|
|
}
|
|
}
|
|
n_err_last = errors;
|
|
}
|
|
}
|
|
|
|
// https://varietyofsound.wordpress.com/2011/02/14/efficient-tanh-computation-using-lamberts-continued-fraction/
|
|
// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/10/0001/
|
|
// https://mathr.co.uk/blog/2017-09-06_approximating_hyperbolic_tangent.html
|
|
|
|
|
|
// thank you Douglas Bagnall
|
|
// https://math.stackexchange.com/a/446411
|
|
static 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));
|
|
//float a = x * (10395.0f + x2 * (1260.0f + x2 * 21.0f));
|
|
//float b = 10395.0f + x2 * (4725.0f + x2 * (210.0f + x2));
|
|
float a = x * (945.0f + x2 * (105.0f + x2));
|
|
float b = 945.0f + x2 * (420.0f + x2 * 15.0f);
|
|
return a / b;
|
|
}
|
|
|
|
|
|
static float fast_atanh(float x) {
|
|
float x2 = x * x;
|
|
//float a = x * (-15015.0f + x2 * (19250.0f + x2 * (-5943.0f + x2 * 256.0f)));
|
|
//float b = (-15015.0f + x2 * (24255.0f + x2 * (-11025.0f + x2 * 1225.0f)));
|
|
//float a = x * (-1155.0f + x2 * (1190.0f + x2 * -231.0f));
|
|
//float b = (-1155.0f + x2 * (1575.0f + x2 * (-525.0f + x2 * 25.0f)));
|
|
float a = x * (945.0f + x2 * (-735.0f + x2 * 64.0f));
|
|
float b = (945.0f + x2 * (-1050.0f + x2 * 225.0f));
|
|
return a / b;
|
|
}
|
|
|
|
|
|
static float pltanh(float x) {
|
|
float isign = +1;
|
|
if (x < 0) {
|
|
isign = -1;
|
|
x = -x;
|
|
}
|
|
if (x < 0.8f) {
|
|
return isign * 0.83 * x;
|
|
}
|
|
if (x < 1.6f) {
|
|
return isign * (0.322f * x + 0.4064f);
|
|
}
|
|
if (x < 3.0f) {
|
|
return isign * (0.0524f * x + 0.8378f);
|
|
}
|
|
if (x < 7.0f) {
|
|
return isign * (0.0012f * x + 0.9914f);
|
|
}
|
|
return isign*0.9998f;
|
|
}
|
|
|
|
|
|
static float platanh(float x) {
|
|
float isign = +1;
|
|
if (x < 0) {
|
|
isign = -1;
|
|
x = -x;
|
|
}
|
|
if (x < 0.664f) {
|
|
return isign * x / 0.83f;
|
|
}
|
|
if (x < 0.9217f) {
|
|
return isign * (x - 0.4064f) / 0.322f;
|
|
}
|
|
if (x < 0.9951f) {
|
|
return isign * (x - 0.8378f) / 0.0524f;
|
|
}
|
|
if (x < 0.9998f) {
|
|
return isign * (x - 0.9914f) / 0.0012f;
|
|
}
|
|
return isign * 7.0f;
|
|
}
|
|
|
|
} // namespace
|