kopia lustrzana https://github.com/F5OEO/ft8_lib
286 wiersze
7.7 KiB
C++
286 wiersze
7.7 KiB
C++
//
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// LDPC decoder for FT8.
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//
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// given a 174-bit codeword as an array of log-likelihood of zero,
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// return a 174-bit corrected codeword, or zero-length array.
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// last 87 bits are the (systematic) plain-text.
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// this is an implementation of the sum-product algorithm
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// from Sarah Johnson's Iterative Error Correction book.
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// codeword[i] = log ( P(x=0) / P(x=1) )
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//
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#include <stdio.h>
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#include <math.h>
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#include <stdlib.h>
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#include "arrays.h"
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int ldpc_check(int codeword[]);
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const int N = 174;
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const int M = 87;
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// https://varietyofsound.wordpress.com/2011/02/14/efficient-tanh-computation-using-lamberts-continued-fraction/
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// http://functions.wolfram.com/ElementaryFunctions/ArcTanh/10/0001/
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// https://mathr.co.uk/blog/2017-09-06_approximating_hyperbolic_tangent.html
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// thank you Douglas Bagnall
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// https://math.stackexchange.com/a/446411
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float fast_tanh(float x) {
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if (x < -4.97f) {
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return -1.0f;
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}
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if (x > 4.97f) {
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return 1.0f;
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}
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float x2 = x * x;
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//float a = x * (135135.0f + x2 * (17325.0f + x2 * (378.0f + x2)));
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//float b = 135135.0f + x2 * (62370.0f + x2 * (3150.0f + x2 * 28.0f));
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//float a = x * (10395.0f + x2 * (1260.0f + x2 * 21.0f));
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//float b = 10395.0f + x2 * (4725.0f + x2 * (210.0f + x2));
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float a = x * (945.0f + x2 * (105.0f + x2));
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float b = 945.0f + x2 * (420.0f + x2 * 15.0f);
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return a / b;
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}
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float fast_atanh(float x) {
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float x2 = x * x;
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//float a = x * (-15015.0f + x2 * (19250.0f + x2 * (-5943.0f + x2 * 256.0f)));
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//float b = (-15015.0f + x2 * (24255.0f + x2 * (-11025.0f + x2 * 1225.0f)));
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//float a = x * (-1155.0f + x2 * (1190.0f + x2 * -231.0f));
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//float b = (-1155.0f + x2 * (1575.0f + x2 * (-525.0f + x2 * 25.0f)));
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float a = x * (945.0f + x2 * (-735.0f + x2 * 64.0f));
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float b = (945.0f + x2 * (-1050.0f + x2 * 225.0f));
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return a / b;
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}
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float pltanh(float x) {
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float isign = +1;
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if (x < 0) {
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isign = -1;
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x = -x;
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}
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if (x < 0.8f) {
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return isign * 0.83 * x;
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}
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if (x < 1.6f) {
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return isign * (0.322f * x + 0.4064f);
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}
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if (x < 3.0f) {
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return isign * (0.0524f * x + 0.8378f);
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}
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if (x < 7.0f) {
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return isign * (0.0012f * x + 0.9914f);
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}
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return isign*0.9998f;
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}
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float platanh(float x) {
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float isign = +1;
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if (x < 0) {
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isign = -1;
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x = -x;
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}
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if (x < 0.664f) {
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return isign * x / 0.83f;
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}
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if (x < 0.9217f) {
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return isign * (x - 0.4064f) / 0.322f;
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}
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if (x < 0.9951f) {
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return isign * (x - 0.8378f) / 0.0524f;
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}
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if (x < 0.9998f) {
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return isign * (x - 0.9914f) / 0.0012f;
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}
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return isign * 7.0f;
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}
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// codeword is 174 log-likelihoods.
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// plain is a return value, 174 ints, to be 0 or 1.
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// max_iters is how hard to try.
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// ok == 87 means success.
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void ldpc_decode(float codeword[], int max_iters, int plain[], int *ok) {
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float m[M][N]; // ~60 kB
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float e[M][N]; // ~60 kB
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int best_score = -1;
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for (int j = 0; j < M; j++) {
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for (int i = 0; i < N; i++) {
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m[j][i] = codeword[i];
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e[j][i] = 0.0f;
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}
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}
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for (int iter = 0; iter < max_iters; iter++) {
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for (int j = 0; j < M; j++) {
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for (int ii1 = 0; ii1 < nrw[j]; ii1++) {
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int i1 = Nm[j][ii1] - 1;
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float a = 1.0f;
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for (int ii2 = 0; ii2 < nrw[j]; ii2++) {
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int i2 = Nm[j][ii2] - 1;
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if (i2 != i1) {
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a *= fast_tanh(-m[j][i2] / 2.0f);
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}
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}
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e[j][i1] = logf((1 - a) / (1 + a));
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}
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}
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int cw[N];
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for (int i = 0; i < N; i++) {
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float l = codeword[i];
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for (int j = 0; j < 3; j++)
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l += e[Mn[i][j] - 1][i];
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cw[i] = (l > 0) ? 1 : 0;
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}
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int score = ldpc_check(cw);
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if (score > best_score) {
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for (int i = 0; i < N; i++) {
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plain[i] = cw[colorder[i]];
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}
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best_score = score;
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if (score == M) {
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// Found a perfect answer
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break;
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}
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}
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for (int i = 0; i < N; i++) {
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for (int ji1 = 0; ji1 < 3; ji1++) {
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int j1 = Mn[i][ji1] - 1;
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float l = codeword[i];
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for (int ji2 = 0; ji2 < 3; ji2++) {
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if (ji1 != ji2) {
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int j2 = Mn[i][ji2] - 1;
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l += e[j2][i];
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}
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}
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m[j1][i] = l;
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}
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}
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}
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*ok = best_score;
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}
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//
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// does a 174-bit codeword pass the FT8's LDPC parity checks?
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// returns the number of parity checks that passed.
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// 87 means total success.
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//
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int ldpc_check(int codeword[]) {
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int score = 0;
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// Nm[87][7]
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for (int j = 0; j < M; ++j) {
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int x = 0;
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for (int ii1 = 0; ii1 < nrw[j]; ++ii1) {
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x ^= codeword[Nm[j][ii1] - 1];
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}
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if (x == 0) {
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++score;
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}
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}
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return score;
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}
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void bp_decode(float codeword[], int max_iters, int plain[], int *ok) {
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float tov[N][3];
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float toc[M][7];
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int best_score = -1;
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int nclast = 0;
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int ncnt = 0;
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// initialize messages to checks
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for (int i = 0; i < M; ++i) {
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for (int j = 0; j < nrw[i]; ++j) {
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toc[i][j] = codeword[Nm[i][j] - 1];
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}
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}
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for (int i = 0; i < N; ++i) {
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for (int j = 0; j < 3; ++j) {
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tov[i][j] = 0;
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}
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}
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for (int iter = 0; iter < max_iters; ++iter) {
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float zn[N];
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int cw[N];
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// Update bit log likelihood ratios (tov=0 in iter 0)
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for (int i = 0; i < N; ++i) {
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zn[i] = codeword[i] + tov[i][0] + tov[i][1] + tov[i][2];
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cw[i] = (zn[i] > 0) ? 1 : 0;
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}
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// Check to see if we have a codeword (check before we do any iter)
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int score = ldpc_check(cw);
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if (score > best_score) {
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// we have a better guess - reorder the columns and store it
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for (int i = 0; i < N; i++) {
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plain[i] = cw[colorder[i]];
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}
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best_score = score;
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if (score == M) {
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break;
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}
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}
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// Send messages from bits to check nodes
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for (int i = 0; i < M; ++i) {
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for (int j = 0; j < nrw[i]; ++j) {
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int ibj = Nm[i][j] - 1;
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toc[i][j] = zn[ibj];
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for (int kk = 0; kk < 3; ++kk) {
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// subtract off what the bit had received from the check
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if (Mn[ibj][kk] - 1 == i) {
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toc[i][j] -= tov[ibj][kk];
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}
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}
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}
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}
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// send messages from check nodes to variable nodes
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for (int i = 0; i < M; ++i) {
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for (int j = 0; j < nrw[i]; ++j) {
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//toc[i][j] = pltanh(-toc[i][j] / 2);
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toc[i][j] = fast_tanh(-toc[i][j] / 2);
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//toc[i][j] = tanhf(-toc[i][j] / 2);
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}
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}
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for (int i = 0; i < N; ++i) {
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for (int j = 0; j < 3; ++j) {
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int ichk = Mn[i][j] - 1; // Mn(:,j) are the checks that include bit j
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float Tmn = 1.0f;
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for (int k = 0; k < nrw[ichk]; ++k) {
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if (Nm[ichk][k] - 1 != i) {
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Tmn *= toc[ichk][k];
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}
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}
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//tov[i][j] = 2 * platanh(-Tmn);
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tov[i][j] = 2 * fast_atanh(-Tmn);
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//tov[i][j] = 2 * atanhf(-Tmn);
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}
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}
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}
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*ok = best_score;
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}
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