/* Regression Test for the Low-density parity-check Encoder and Decoder Table entries below copied from: https://www.etsi.org/deliver/etsi_en/302700_302799/302755/01.04.01_60/en_302755v010401p.pdf Copyright 2018 Ahmet Inan */ #include #include #include #include #include #include #include #include "ldpc_encoder.hh" #include "ldpc_decoder.hh" struct DVB_T2_TABLE_A1 { static const int M = 360; static const int N = 64800; static const int K = 32400; static const int LINKS_MIN_CN = 6; static const int LINKS_MAX_CN = 7; static const int LINKS_TOTAL = 226799; static const int DEG_MAX = 8; static constexpr int DEG[] = { 8, 3, 0 }; static constexpr int LEN[] = { 36, 54, 0 }; static constexpr int POS[] = { 54, 9318, 14392, 27561, 26909, 10219, 2534, 8597, 55, 7263, 4635, 2530, 28130, 3033, 23830, 3651, 56, 24731, 23583, 26036, 17299, 5750, 792, 9169, 57, 5811, 26154, 18653, 11551, 15447, 13685, 16264, 58, 12610, 11347, 28768, 2792, 3174, 29371, 12997, 59, 16789, 16018, 21449, 6165, 21202, 15850, 3186, 60, 31016, 21449, 17618, 6213, 12166, 8334, 18212, 61, 22836, 14213, 11327, 5896, 718, 11727, 9308, 62, 2091, 24941, 29966, 23634, 9013, 15587, 5444, 63, 22207, 3983, 16904, 28534, 21415, 27524, 25912, 64, 25687, 4501, 22193, 14665, 14798, 16158, 5491, 65, 4520, 17094, 23397, 4264, 22370, 16941, 21526, 66, 10490, 6182, 32370, 9597, 30841, 25954, 2762, 67, 22120, 22865, 29870, 15147, 13668, 14955, 19235, 68, 6689, 18408, 18346, 9918, 25746, 5443, 20645, 69, 29982, 12529, 13858, 4746, 30370, 10023, 24828, 70, 1262, 28032, 29888, 13063, 24033, 21951, 7863, 71, 6594, 29642, 31451, 14831, 9509, 9335, 31552, 72, 1358, 6454, 16633, 20354, 24598, 624, 5265, 73, 19529, 295, 18011, 3080, 13364, 8032, 15323, 74, 11981, 1510, 7960, 21462, 9129, 11370, 25741, 75, 9276, 29656, 4543, 30699, 20646, 21921, 28050, 76, 15975, 25634, 5520, 31119, 13715, 21949, 19605, 77, 18688, 4608, 31755, 30165, 13103, 10706, 29224, 78, 21514, 23117, 12245, 26035, 31656, 25631, 30699, 79, 9674, 24966, 31285, 29908, 17042, 24588, 31857, 80, 21856, 27777, 29919, 27000, 14897, 11409, 7122, 81, 29773, 23310, 263, 4877, 28622, 20545, 22092, 82, 15605, 5651, 21864, 3967, 14419, 22757, 15896, 83, 30145, 1759, 10139, 29223, 26086, 10556, 5098, 84, 18815, 16575, 2936, 24457, 26738, 6030, 505, 85, 30326, 22298, 27562, 20131, 26390, 6247, 24791, 86, 928, 29246, 21246, 12400, 15311, 32309, 18608, 87, 20314, 6025, 26689, 16302, 2296, 3244, 19613, 88, 6237, 11943, 22851, 15642, 23857, 15112, 20947, 89, 26403, 25168, 19038, 18384, 8882, 12719, 7093, 0, 14567, 24965, 1, 3908, 100, 2, 10279, 240, 3, 24102, 764, 4, 12383, 4173, 5, 13861, 15918, 6, 21327, 1046, 7, 5288, 14579, 8, 28158, 8069, 9, 16583, 11098, 10, 16681, 28363, 11, 13980, 24725, 12, 32169, 17989, 13, 10907, 2767, 14, 21557, 3818, 15, 26676, 12422, 16, 7676, 8754, 17, 14905, 20232, 18, 15719, 24646, 19, 31942, 8589, 20, 19978, 27197, 21, 27060, 15071, 22, 6071, 26649, 23, 10393, 11176, 24, 9597, 13370, 25, 7081, 17677, 26, 1433, 19513, 27, 26925, 9014, 28, 19202, 8900, 29, 18152, 30647, 30, 20803, 1737, 31, 11804, 25221, 32, 31683, 17783, 33, 29694, 9345, 34, 12280, 26611, 35, 6526, 26122, 36, 26165, 11241, 37, 7666, 26962, 38, 16290, 8480, 39, 11774, 10120, 40, 30051, 30426, 41, 1335, 15424, 42, 6865, 17742, 43, 31779, 12489, 44, 32120, 21001, 45, 14508, 6996, 46, 979, 25024, 47, 4554, 21896, 48, 7989, 21777, 49, 4972, 20661, 50, 6612, 2730, 51, 12742, 4418, 52, 29194, 595, 53, 19267, 20113, }; }; struct DVB_T2_TABLE_B7 { static const int M = 360; static const int N = 16200; static const int K = 13320; static const int LINKS_MIN_CN = 15; static const int LINKS_MAX_CN = 19; static const int LINKS_TOTAL = 49319; static const int DEG_MAX = 13; static constexpr int DEG[] = { 13, 3, 0 }; static constexpr int LEN[] = { 1, 36, 0 }; static constexpr int POS[] = { 3, 2409, 499, 1481, 908, 559, 716, 1270, 333, 2508, 2264, 1702, 2805, 4, 2447, 1926, 5, 414, 1224, 6, 2114, 842, 7, 212, 573, 0, 2383, 2112, 1, 2286, 2348, 2, 545, 819, 3, 1264, 143, 4, 1701, 2258, 5, 964, 166, 6, 114, 2413, 7, 2243, 81, 0, 1245, 1581, 1, 775, 169, 2, 1696, 1104, 3, 1914, 2831, 4, 532, 1450, 5, 91, 974, 6, 497, 2228, 7, 2326, 1579, 0, 2482, 256, 1, 1117, 1261, 2, 1257, 1658, 3, 1478, 1225, 4, 2511, 980, 5, 2320, 2675, 6, 435, 1278, 7, 228, 503, 0, 1885, 2369, 1, 57, 483, 2, 838, 1050, 3, 1231, 1990, 4, 1738, 68, 5, 2392, 951, 6, 163, 645, 7, 2644, 1704, }; }; constexpr int DVB_T2_TABLE_A1::DEG[]; constexpr int DVB_T2_TABLE_A1::LEN[]; constexpr int DVB_T2_TABLE_A1::POS[]; constexpr int DVB_T2_TABLE_B7::DEG[]; constexpr int DVB_T2_TABLE_B7::LEN[]; constexpr int DVB_T2_TABLE_B7::POS[]; #if 0 typedef DVB_T2_TABLE_A1 TABLE; static const float QEF_SNR = -1.8; static const int BCH_T = 12; #else typedef DVB_T2_TABLE_B7 TABLE; static const float QEF_SNR = 2.5; static const int BCH_T = 12; #endif int main() { const int TRIALS = 25; const int FACTOR = 2; const int BETA = 1; const int CODE_LEN = TABLE::N; const int DATA_LEN = TABLE::K; CODE::LDPCEncoder encode; CODE::LDPCDecoder decode; std::random_device rd; std::default_random_engine generator(rd()); typedef std::uniform_int_distribution uniform; typedef std::normal_distribution normal; int8_t *code = new int8_t[CODE_LEN]; int8_t *orig = new int8_t[CODE_LEN]; int8_t *noisy = new int8_t[CODE_LEN]; float *symb = new float[CODE_LEN]; float min_SNR = 20, min_mbs = 1000, max_mbs = 0; for (float SNR = -5; SNR <= 15; SNR += 0.1) { float mean = 1; float sigma = std::sqrt(mean * mean / (2 * std::pow(10, SNR / 10))); auto data = std::bind(uniform(0, 1), generator); auto awgn = std::bind(normal(0.0, sigma), generator); for (int i = 0; i < DATA_LEN; ++i) code[i] = 1 - 2 * data(); encode(code, code + DATA_LEN); for (int i = 0; i < CODE_LEN; ++i) orig[i] = code[i]; for (int i = 0; i < CODE_LEN; ++i) symb[i] = code[i]; for (int i = 0; i < CODE_LEN; ++i) symb[i] += awgn(); // $LLR=log(\frac{p(x=+1|y)}{p(x=-1|y)})$ // $p(x|\mu,\sigma)=\frac{1}{\sqrt{2\pi}\sigma}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$ float DIST = 2; // BPSK float fact = DIST * FACTOR / (sigma * sigma); for (int i = 0; i < CODE_LEN; ++i) code[i] = std::min(std::max(std::nearbyint(fact * symb[i]), -128), 127); for (int i = 0; i < CODE_LEN; ++i) noisy[i] = code[i]; auto start = std::chrono::system_clock::now(); int count = decode(code, code + DATA_LEN, TRIALS); auto end = std::chrono::system_clock::now(); auto usec = std::chrono::duration_cast(end - start); float mbs = (float)DATA_LEN / usec.count(); int iters = count < 0 ? TRIALS : TRIALS - count; int awgn_errors = 0; for (int i = 0; i < CODE_LEN; ++i) awgn_errors += noisy[i] * orig[i] < 0; int quantization_erasures = 0; for (int i = 0; i < CODE_LEN; ++i) quantization_erasures += !noisy[i]; int uncorrected_errors = 0; for (int i = 0; i < CODE_LEN; ++i) uncorrected_errors += code[i] * orig[i] <= 0; int decoder_errors = 0; for (int i = 0; i < CODE_LEN; ++i) decoder_errors += code[i] * orig[i] <= 0 && orig[i] * noisy[i] > 0; float bit_error_rate = (float)uncorrected_errors / (float)(CODE_LEN); if (uncorrected_errors <= BCH_T) min_SNR = std::min(min_SNR, SNR); min_mbs = std::min(min_mbs, mbs); max_mbs = std::max(max_mbs, mbs); if (0) { std::cerr << SNR << " Es/N0 => standard deviation of " << sigma << " with mean " << mean << std::endl; std::cerr << awgn_errors << " errors caused by AWGN." << std::endl; std::cerr << quantization_erasures << " erasures caused by quantization." << std::endl; std::cerr << decoder_errors << " errors caused by decoder." << std::endl; std::cerr << uncorrected_errors << " errors uncorrected." << std::endl; std::cerr << bit_error_rate << " bit error rate." << std::endl; if (count < 0) { std::cerr << "decoder failed at converging to a code word!" << std::endl; } else { std::cerr << iters << " iterations were needed." << std::endl; } std::cerr << usec.count() << " microseconds to decode." << std::endl; std::cerr << mbs << " megabit per second." << std::endl; } else { std::cout << SNR << " " << bit_error_rate << " " << iters << " " << mbs << std::endl; } } delete[] code; delete[] orig; delete[] noisy; delete[] symb; std::cerr << "QEF at: " << min_SNR << " SNR, speed min: " << min_mbs << " Mb/s and speed max: " << max_mbs << " Mb/s." << std::endl; assert(min_SNR < QEF_SNR); std::cerr << "Low-density parity-check code regression test passed!" << std::endl; return 0; }