/////////////////////////////////////////////////////////////////////////////////// // Copyright (C) 2023 Edouard Griffiths, F4EXB // // // // 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 . // /////////////////////////////////////////////////////////////////////////////////// // // ordered statistics decoder for LDPC and new FT8. // idea from wsjt-x. // #include #include #include #include "libldpc.h" #include "osd.h" namespace FT8 { // // check the FT8 CRC-14 // int OSD::check_crc(const int a91[91]) { int aa[91]; int non_zero = 0; for (int i = 0; i < 91; i++) { if (i < 77) { aa[i] = a91[i]; } else { aa[i] = 0; } if (aa[i]) non_zero++; } int out1[14]; // don't bother with all-zero messages. if (non_zero == 0) return 0; // why 82? why not 77? LDPC::ft8_crc(aa, 82, out1); for (int i = 0; i < 14; i++) { if (out1[i] != a91[91 - 14 + i]) { return 0; } } return 1; } // plain is 91 bits of plain-text. // returns a 174-bit codeword. // mimics wsjt-x's encode174_91.f90. void OSD::ldpc_encode(int plain[91], int codeword[174]) { // the systematic 91 bits. for (int i = 0; i < 91; i++) { codeword[i] = plain[i]; } // the 174-91 bits of redundancy. for (int i = 0; i + 91 < 174; i++) { int sum = 0; for (int j = 0; j < 91; j++) { sum += gen_sys[i + 91][j] * plain[j]; codeword[i + 91] = sum % 2; } } } // xplain is a possible original codeword. // ll174 is what was received. // ldpc-encode xplain; how close is the // result to what we received? float OSD::osd_score(int xplain[91], float ll174[174]) { int xcode[174]; ldpc_encode(xplain, xcode); float score = 0; for (int i = 0; i < 174; i++) { if (xcode[i]) { // one-bit, expect ll to be negative. score -= ll174[i] * 4.6; } else { // zero-bit, expect ll to be positive. score += ll174[i] * 4.6; } } return -score; } // does a decode look plausible? int OSD::osd_check(const int plain[91]) { int allzero = 1; for (int i = 0; i < 91; i++) { if (plain[i] != 0) { allzero = 0; } } if (allzero) { return 0; } if (check_crc(plain) == 0) { return 0; } return 1; } void OSD::matmul(int a[91][91], int b[91], int c[91]) { for (int i = 0; i < 91; i++) { int sum = 0; for (int j = 0; j < 91; j++) { sum += a[i][j] * b[j]; } c[i] = sum % 2; } } // ordered statistics decoder for LDPC and new FT8. // idea from wsjt-x. // codeword[i] = log ( P(x=0) / P(x=1) ) // codeword has 174 bits. // first 91 bits are plaintext, remaining 83 are parity. // returns 0 or 1, with decoded plain bits in out91[]. // and actual depth used in *out_depth. int OSD::osd_decode(float codeword[174], int depth, int out[91], int *out_depth) { // strength = abs(codeword) float strength[174]; for (int i = 0; i < 174; i++) { float x = codeword[i]; strength[i] = (x < 0 ? -x : x); } // sort, strongest first; we'll use strongest 91. std::vector which(174); for (int i = 0; i < 174; i++) { which[i] = i; } std::sort( which.begin(), which.end(), [=](int a, int b) { return strength[a] > strength[b]; } ); // gen_sys[174 rows][91 cols] has a row per each of the 174 codeword bits, // indicating how to generate it by xor with each of the 91 plain bits. // generator matrix, reordered strongest codeword bit first. int b[174][91 * 2]; for (int i = 0; i < 174; i++) { int ii = which[i]; for (int j = 0; j < 91 * 2; j++) { if (j < 91) { b[i][j] = gen_sys[ii][j]; } else { b[i][j] = 0; } } } int xwhich[174]; for (int i = 0; i < 174; i++) { xwhich[i] = which[i]; } int ok = 0; LDPC::gauss_jordan(91, 174, b, xwhich, &ok); if (ok == 0) { fprintf(stderr, "gauss_jordan failed\n"); } int gen1_inv[91][91]; for (int i = 0; i < 91; i++) { for (int j = 0; j < 91; j++) { gen1_inv[i][j] = b[i][91 + j]; } } for (int i = 0; i < 174; i++) { which[i] = xwhich[i]; } // y1 is the received bits, same order as gen1_inv, // more or less strongest-first, converted from // log-likihood to 0/1. int y1[91]; for (int i = 0; i < 91; i++) { int j = which[i]; y1[i] = (codeword[j] < 0 ? 1 : 0); } int best_plain[91]; float best_score = 0; int got_a_best = 0; int best_depth = -1; // can we decode without flipping any bits? int xplain[91]; matmul(gen1_inv, y1, xplain); // also does mod 2 int osd_thresh = -500; float xscore = osd_score(xplain, codeword); int ch = osd_check(xplain); if (xscore < osd_thresh && ch) { if (got_a_best == 0 || xscore < best_score) { if (1) { // just accept this, since no bits had to be flipped. std::copy(xplain, xplain + 91, out); *out_depth = 0; return 1; } else { got_a_best = 1; std::copy(xplain, xplain + 91, best_plain); best_score = xscore; best_depth = 0; } } } // flip a few bits, see if decode works. for (int ii = 0; ii < depth; ii++) { int i = 91 - 1 - ii; y1[i] ^= 1; matmul(gen1_inv, y1, xplain); y1[i] ^= 1; float xscore = osd_score(xplain, codeword); int ch = osd_check(xplain); if (xscore < osd_thresh && ch) { if (got_a_best == 0 || xscore < best_score) { got_a_best = 1; std::copy(xplain, xplain + 91, best_plain); best_score = xscore; best_depth = ii; } } } if (got_a_best) { std::copy(best_plain, best_plain + 91, out); *out_depth = best_depth; return 1; } else { return 0; } } const int OSD::gen_sys[174][91] = { { 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, { 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, }, { 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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