Fox's Git Mirrors
Commit fbd253aff41e00c3c5b047eb6ecc2c7de5e97596
Parents : 2f4d090
Author : Ahmet Inan <inan@aicodix.de>
Date : 2025-12-22T12:54:26+01:00
prepare for Polarization-Adjusted Convolutional codes
Changes
3 files changed, 582 insertions(+), 0 deletions(-)
Diff
diff --git a/pac_encoder.hh b/pac_encoder.hh
new file mode 100644
index 0000000..b358391
--- /dev/null
+++ b/pac_encoder.hh
@@ -0,0 +1,39 @@
+/*
+Encoder for Polarization-Adjusted Convolutional codes
+
+Copyright 2025 Ahmet Inan <inan@aicodix.de>
+*/
+
+#pragma once
+
+#include "polar_helper.hh"
+
+namespace CODE {
+
+template <typename TYPE>
+class PACEncoder
+{
+ typedef PolarHelper<TYPE> PH;
+ static bool get(const uint32_t *bits, int idx)
+ {
+ return (bits[idx/32] >> (idx%32)) & 1;
+ }
+public:
+ void operator()(TYPE *codeword, const TYPE *message, const uint32_t *frozen, int level)
+ {
+ int length = 1 << level;
+ for (int i = 0; i < length; i += 2) {
+ TYPE msg0 = get(frozen, i) ? PH::one() : *message++;
+ TYPE msg1 = get(frozen, i+1) ? PH::one() : *message++;
+ codeword[i] = PH::qmul(msg0, msg1);
+ codeword[i+1] = msg1;
+ }
+ for (int h = 2; h < length; h *= 2)
+ for (int i = 0; i < length; i += 2 * h)
+ for (int j = i; j < i + h; ++j)
+ codeword[j] = PH::qmul(codeword[j], codeword[j+h]);
+ }
+};
+
+}
+
diff --git a/pac_list_decoder.hh b/pac_list_decoder.hh
new file mode 100644
index 0000000..29b3720
--- /dev/null
+++ b/pac_list_decoder.hh
@@ -0,0 +1,327 @@
+/*
+List decoding of Polarization-Adjusted Convolutional codes
+
+Copyright 2025 Ahmet Inan <inan@aicodix.de>
+*/
+
+#pragma once
+
+#include "sort.hh"
+#include "polar_helper.hh"
+
+namespace CODE {
+
+template <typename TYPE, int M>
+struct PACListNode
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static const int N = 1 << M;
+ static MAP rate0(PATH *metric, TYPE *hard, TYPE *soft)
+ {
+ for (int i = 0; i < N; ++i)
+ hard[i] = PH::one();
+ for (int i = 0; i < N; ++i)
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ if (soft[i+N].v[k] < 0)
+ metric[k] -= soft[i+N].v[k];
+ MAP map;
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ map.v[k] = k;
+ return map;
+ }
+};
+
+template <typename TYPE>
+struct PACListNode<TYPE, 0>
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static MAP rate0(PATH *metric, TYPE *hard, TYPE *soft)
+ {
+ *hard = PH::one();
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ if (soft[1].v[k] < 0)
+ metric[k] -= soft[1].v[k];
+ MAP map;
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ map.v[k] = k;
+ return map;
+ }
+ static MAP rate1(PATH *metric, TYPE *message, MAP *maps, int *count, TYPE *hard, TYPE *soft)
+ {
+ TYPE sft = soft[1];
+ PATH fork[2*TYPE::SIZE];
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ fork[2*k] = fork[2*k+1] = metric[k];
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ if (sft.v[k] < 0)
+ fork[2*k] -= sft.v[k];
+ else
+ fork[2*k+1] += sft.v[k];
+ int perm[2*TYPE::SIZE];
+ CODE::insertion_sort(perm, fork, 2*TYPE::SIZE);
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ metric[k] = fork[k];
+ MAP map;
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ map.v[k] = perm[k] >> 1;
+ TYPE hrd;
+ for (int k = 0; k < TYPE::SIZE; ++k)
+ hrd.v[k] = 1 - 2 * (perm[k] & 1);
+ message[*count] = hrd;
+ maps[*count] = map;
+ ++*count;
+ *hard = hrd;
+ return map;
+ }
+};
+
+template <typename TYPE, int M>
+struct PACListTree
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static const int N = 1 << M;
+ static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *count, TYPE *hard, TYPE *soft, const uint32_t *frozen)
+ {
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
+ MAP lmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard, soft, frozen);
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
+ MAP rmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard+N/2, soft, frozen+N/2/32);
+ for (int i = 0; i < N/2; ++i)
+ hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
+ return vshuf(lmap, rmap);
+ }
+};
+
+template <typename TYPE>
+struct PACListTree<TYPE, 6>
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static const int M = 6;
+ static const int N = 1 << M;
+ static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *count, TYPE *hard, TYPE *soft, const uint32_t *frozen)
+ {
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
+ MAP lmap, rmap;
+ if (frozen[0] == 0xffffffff)
+ lmap = PACListNode<TYPE, M-1>::rate0(metric, hard, soft);
+ else
+ lmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard, soft, frozen[0]);
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
+ if (frozen[1] == 0xffffffff)
+ rmap = PACListNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
+ else
+ rmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard+N/2, soft, frozen[1]);
+ for (int i = 0; i < N/2; ++i)
+ hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
+ return vshuf(lmap, rmap);
+ }
+};
+
+template <typename TYPE>
+struct PACListTree<TYPE, 5>
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static const int M = 5;
+ static const int N = 1 << M;
+ static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *count, TYPE *hard, TYPE *soft, uint32_t frozen)
+ {
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
+ MAP lmap, rmap;
+ if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
+ lmap = PACListNode<TYPE, M-1>::rate0(metric, hard, soft);
+ else
+ lmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard, soft, frozen & ((1<<(1<<(M-1)))-1));
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
+ if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
+ rmap = PACListNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
+ else
+ rmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard+N/2, soft, frozen >> (N/2));
+ for (int i = 0; i < N/2; ++i)
+ hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
+ return vshuf(lmap, rmap);
+ }
+};
+
+template <typename TYPE>
+struct PACListTree<TYPE, 4>
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static const int M = 4;
+ static const int N = 1 << M;
+ static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *count, TYPE *hard, TYPE *soft, uint32_t frozen)
+ {
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
+ MAP lmap, rmap;
+ if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
+ lmap = PACListNode<TYPE, M-1>::rate0(metric, hard, soft);
+ else
+ lmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard, soft, frozen & ((1<<(1<<(M-1)))-1));
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
+ if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
+ rmap = PACListNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
+ else
+ rmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard+N/2, soft, frozen >> (N/2));
+ for (int i = 0; i < N/2; ++i)
+ hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
+ return vshuf(lmap, rmap);
+ }
+};
+
+template <typename TYPE>
+struct PACListTree<TYPE, 3>
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static const int M = 3;
+ static const int N = 1 << M;
+ static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *count, TYPE *hard, TYPE *soft, uint32_t frozen)
+ {
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
+ MAP lmap, rmap;
+ if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
+ lmap = PACListNode<TYPE, M-1>::rate0(metric, hard, soft);
+ else
+ lmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard, soft, frozen & ((1<<(1<<(M-1)))-1));
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
+ if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
+ rmap = PACListNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
+ else
+ rmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard+N/2, soft, frozen >> (N/2));
+ for (int i = 0; i < N/2; ++i)
+ hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
+ return vshuf(lmap, rmap);
+ }
+};
+
+template <typename TYPE>
+struct PACListTree<TYPE, 2>
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static const int M = 2;
+ static const int N = 1 << M;
+ static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *count, TYPE *hard, TYPE *soft, uint32_t frozen)
+ {
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::prod(soft[i+N], soft[i+N/2+N]);
+ MAP lmap, rmap;
+ if ((frozen & ((1<<(1<<(M-1)))-1)) == ((1<<(1<<(M-1)))-1))
+ lmap = PACListNode<TYPE, M-1>::rate0(metric, hard, soft);
+ else
+ lmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard, soft, frozen & ((1<<(1<<(M-1)))-1));
+ for (int i = 0; i < N/2; ++i)
+ soft[i+N/2] = PH::madd(hard[i], vshuf(soft[i+N], lmap), vshuf(soft[i+N/2+N], lmap));
+ if (frozen >> (N/2) == ((1<<(1<<(M-1)))-1))
+ rmap = PACListNode<TYPE, M-1>::rate0(metric, hard+N/2, soft);
+ else
+ rmap = PACListTree<TYPE, M-1>::decode(metric, message, maps, count, hard+N/2, soft, frozen >> (N/2));
+ for (int i = 0; i < N/2; ++i)
+ hard[i] = PH::qmul(vshuf(hard[i], rmap), hard[i+N/2]);
+ return vshuf(lmap, rmap);
+ }
+};
+
+template <typename TYPE>
+struct PACListTree<TYPE, 1>
+{
+ typedef PolarHelper<TYPE> PH;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static MAP decode(PATH *metric, TYPE *message, MAP *maps, int *count, TYPE *hard, TYPE *soft, uint32_t frozen)
+ {
+ soft[1] = PH::prod(soft[2], soft[3]);
+ MAP lmap, rmap;
+ if (frozen & 1)
+ lmap = PACListNode<TYPE, 0>::rate0(metric, hard, soft);
+ else
+ lmap = PACListNode<TYPE, 0>::rate1(metric, message, maps, count, hard, soft);
+ soft[1] = PH::madd(hard[0], vshuf(soft[2], lmap), vshuf(soft[3], lmap));
+ if (frozen >> 1)
+ rmap = PACListNode<TYPE, 0>::rate0(metric, hard+1, soft);
+ else
+ rmap = PACListNode<TYPE, 0>::rate1(metric, message, maps, count, hard+1, soft);
+ hard[0] = PH::qmul(vshuf(hard[0], rmap), hard[1]);
+ return vshuf(lmap, rmap);
+ }
+};
+
+template <typename TYPE, int MAX_M>
+class PACListDecoder
+{
+ static_assert(MAX_M >= 5 && MAX_M <= 16);
+ typedef PolarHelper<TYPE> PH;
+ typedef typename TYPE::value_type VALUE;
+ typedef typename PH::PATH PATH;
+ typedef typename PH::MAP MAP;
+ static const int MAX_N = 1 << MAX_M;
+ TYPE soft[2*MAX_N];
+ TYPE hard[MAX_N];
+ MAP maps[MAX_N];
+public:
+ void operator()(int *rank, TYPE *message, const VALUE *codeword, const uint32_t *frozen, int level)
+ {
+ assert(level <= MAX_M);
+ PATH metric[TYPE::SIZE];
+ int count = 0;
+ metric[0] = 0;
+ for (int k = 1; k < TYPE::SIZE; ++k)
+ metric[k] = 1000000;
+ int length = 1 << level;
+ for (int i = 0; i < length; ++i)
+ soft[length+i] = vdup<TYPE>(codeword[i]);
+
+ switch (level) {
+ case 5: PACListTree<TYPE, 5>::decode(metric, message, maps, &count, hard, soft, *frozen); break;
+ case 6: PACListTree<TYPE, 6>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 7: PACListTree<TYPE, 7>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 8: PACListTree<TYPE, 8>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 9: PACListTree<TYPE, 9>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 10: PACListTree<TYPE, 10>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 11: PACListTree<TYPE, 11>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 12: PACListTree<TYPE, 12>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 13: PACListTree<TYPE, 13>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 14: PACListTree<TYPE, 14>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 15: PACListTree<TYPE, 15>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ case 16: PACListTree<TYPE, 16>::decode(metric, message, maps, &count, hard, soft, frozen); break;
+ default: assert(false);
+ }
+
+ for (int i = 0, r = 0; rank != nullptr && i < TYPE::SIZE; ++i) {
+ if (i > 0 && metric[i-1] != metric[i])
+ ++r;
+ rank[i] = r;
+ }
+ MAP acc = maps[count-1];
+ for (int i = count-2; i >= 0; --i) {
+ message[i] = vshuf(message[i], acc);
+ acc = vshuf(maps[i], acc);
+ }
+ }
+};
+
+}
+
diff --git a/tests/pac_list_regression_test.cc b/tests/pac_list_regression_test.cc
new file mode 100644
index 0000000..c41faf5
--- /dev/null
+++ b/tests/pac_list_regression_test.cc
@@ -0,0 +1,216 @@
+/*
+Regression Test for the Polarization-Adjusted Convolutional Encoder and List Decoder
+
+Copyright 2025 Ahmet Inan <inan@aicodix.de>
+*/
+
+#include <limits>
+#include <random>
+#include <chrono>
+#include <cassert>
+#include <iomanip>
+#include <iostream>
+#include <algorithm>
+#include <functional>
+#include "polar_helper.hh"
+#include "pac_list_decoder.hh"
+#include "pac_encoder.hh"
+#include "polar_sequence.hh"
+#include "crc.hh"
+#include "sequence.h"
+
+bool get_bit(const uint32_t *bits, int idx)
+{
+ return (bits[idx/32] >> (idx%32)) & 1;
+}
+
+int main()
+{
+ const int M = 10;
+ const int N = 1 << M;
+ const bool crc_aided = true;
+ CODE::CRC<uint32_t> crc(0xD419CC15);
+ const int C = 32;
+#if 1
+ const int L = 32;
+ typedef int8_t code_type;
+#else
+ const int L = 8;
+ typedef float code_type;
+#endif
+
+ typedef SIMD<code_type, L> simd_type;
+
+ std::random_device rd;
+ typedef std::default_random_engine generator;
+ typedef std::uniform_int_distribution<int> distribution;
+ auto data = std::bind(distribution(0, 1), generator(rd()));
+ auto frozen = new uint32_t[N/32];
+ auto codeword = new code_type[N];
+
+ const int *reliability_sequence;
+ double erasure_probability = 0.3;
+ int K = (1 - erasure_probability) * N;
+ double design_SNR = 10 * std::log10(-std::log(erasure_probability));
+ std::cerr << "design SNR: " << design_SNR << std::endl;
+ if (0) {
+ auto construct = new CODE::PolarSeqConst0<M>;
+ std::cerr << "sizeof(PolarSeqConst0<M>) = " << sizeof(CODE::PolarSeqConst0<M>) << std::endl;
+ double better_SNR = design_SNR + 1.59175;
+ std::cerr << "better SNR: " << better_SNR << std::endl;
+ double probability = std::exp(-pow(10.0, better_SNR / 10));
+ std::cerr << "prob: " << probability << std::endl;
+ auto rel_seq = new int[N];
+ (*construct)(rel_seq, M, probability);
+ delete construct;
+ reliability_sequence = rel_seq;
+ } else {
+ reliability_sequence = sequence;
+ }
+ for (int i = 0; i < N / 32; ++i)
+ frozen[i] = 0;
+ for (int i = 0; i < N - K; ++i)
+ frozen[reliability_sequence[i]/32] |= 1 << (reliability_sequence[i]%32);
+ std::cerr << "Polar(" << N << ", " << K << ")" << std::endl;
+ auto message = new code_type[K];
+ auto decoded = new simd_type[K];
+ std::cerr << "sizeof(PACDecoder<simd_type, M>) = " << sizeof(CODE::PACListDecoder<simd_type, M>) << std::endl;
+ auto decode = new CODE::PACListDecoder<simd_type, M>;
+
+ auto orig = new code_type[N];
+ auto noisy = new code_type[N];
+ auto symb = new double[N];
+ double low_SNR = std::floor(design_SNR-3);
+ double high_SNR = std::ceil(design_SNR+5);
+ double min_SNR = high_SNR, max_mbs = 0;
+ int count = 0;
+ std::cerr << "SNR BER Mbit/s Eb/N0" << std::endl;
+ for (double SNR = low_SNR; count <= 3 && SNR <= high_SNR; SNR += 0.1, ++count) {
+ //double mean_signal = 0;
+ double sigma_signal = 1;
+ double mean_noise = 0;
+ double sigma_noise = std::sqrt(sigma_signal * sigma_signal / (2 * std::pow(10, SNR / 10)));
+
+ typedef std::normal_distribution<double> normal;
+ auto awgn = std::bind(normal(mean_noise, sigma_noise), generator(rd()));
+
+ int64_t awgn_errors = 0;
+ int64_t quantization_erasures = 0;
+ int64_t uncorrected_errors = 0;
+ int64_t ambiguity_erasures = 0;
+ int64_t frame_errors = 0;
+ double avg_mbs = 0;
+ int64_t loops = 0;
+ while (uncorrected_errors < 10000 && ++loops < 1000) {
+ if (crc_aided) {
+ crc.reset();
+ for (int i = 0; i < K-C; ++i) {
+ bool bit = data();
+ crc(bit);
+ message[i] = 1 - 2 * bit;
+ }
+ for (int i = 0; i < C; ++i) {
+ bool bit = (crc() >> i) & 1;
+ message[K-C+i] = 1 - 2 * bit;
+ }
+ } else {
+ for (int i = 0; i < K; ++i)
+ message[i] = 1 - 2 * data();
+ }
+
+ CODE::PACEncoder<code_type> encode;
+ encode(codeword, message, frozen, M);
+
+ for (int i = 0; i < N; ++i)
+ orig[i] = codeword[i];
+
+ for (int i = 0; i < N; ++i)
+ symb[i] = codeword[i];
+
+ for (int i = 0; i < N; ++i)
+ symb[i] += awgn();
+
+ // $LLR=log(\frac{p(x=+1|y)}{p(x=-1|y)})$
+ // $p(x|\mu,\sigma)=\frac{1}{\sqrt{2\pi}\sigma}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$
+ double DIST = 2; // BPSK
+ double fact = DIST / (sigma_noise * sigma_noise);
+ for (int i = 0; i < N; ++i)
+ codeword[i] = CODE::PolarHelper<code_type>::quant(fact * symb[i]);
+
+ for (int i = 0; i < N; ++i)
+ noisy[i] = codeword[i];
+
+ int rank[L];
+ auto start = std::chrono::system_clock::now();
+ (*decode)(rank, decoded, codeword, frozen, M);
+ auto end = std::chrono::system_clock::now();
+ auto usec = std::chrono::duration_cast<std::chrono::microseconds>(end - start);
+ double mbs = (double)K / usec.count();
+ avg_mbs += mbs;
+
+ int best = 0;
+ if (crc_aided) {
+ bool error = true;
+ for (int k = 0; k < L; ++k) {
+ crc.reset();
+ for (int i = 0; i < K; ++i)
+ crc(decoded[i].v[k] < 0);
+ if (crc() == 0) {
+ best = k;
+ error = false;
+ break;
+ }
+ }
+ frame_errors += error;
+ } else {
+ bool error = rank[0] == rank[1];
+ for (int i = 0; i < K; ++i)
+ error |= decoded[i].v[0] * message[i] <= 0;
+ frame_errors += error;
+ }
+
+ for (int i = 0; i < N; ++i)
+ awgn_errors += noisy[i] * (orig[i] < 0);
+ for (int i = 0; i < N; ++i)
+ quantization_erasures += !noisy[i];
+ for (int i = 0; i < K; ++i)
+ uncorrected_errors += decoded[i].v[best] * message[i] <= 0;
+ for (int i = 0; i < K; ++i)
+ ambiguity_erasures += !decoded[i].v[best];
+ }
+
+ avg_mbs /= loops;
+
+ max_mbs = std::max(max_mbs, avg_mbs);
+ double frame_error_rate = (double)frame_errors / (double)loops;
+ double bit_error_rate = (double)uncorrected_errors / (double)(K * loops);
+ if (!uncorrected_errors)
+ min_SNR = std::min(min_SNR, SNR);
+ else
+ count = 0;
+
+ int MOD_BITS = 1; // BPSK
+ double code_rate = (double)K / (double)N;
+ double spectral_efficiency = code_rate * MOD_BITS;
+ double EbN0 = 10 * std::log10(sigma_signal * sigma_signal / (spectral_efficiency * 2 * sigma_noise * sigma_noise));
+
+ if (0) {
+ std::cerr << SNR << " Es/N0 => AWGN with standard deviation of " << sigma_noise << " and mean " << mean_noise << std::endl;
+ std::cerr << EbN0 << " Eb/N0, using spectral efficiency of " << spectral_efficiency << " from " << code_rate << " code rate and " << MOD_BITS << " bits per symbol." << std::endl;
+ std::cerr << awgn_errors << " errors caused by AWGN." << std::endl;
+ std::cerr << quantization_erasures << " erasures caused by quantization." << std::endl;
+ std::cerr << uncorrected_errors << " errors uncorrected." << std::endl;
+ std::cerr << ambiguity_erasures << " ambiguity erasures." << std::endl;
+ std::cerr << frame_error_rate << " frame error rate." << std::endl;
+ std::cerr << bit_error_rate << " bit error rate." << std::endl;
+ std::cerr << avg_mbs << " megabit per second." << std::endl;
+ } else {
+ std::cout << SNR << " " << frame_error_rate << " " << bit_error_rate << " " << avg_mbs << " " << EbN0 << std::endl;
+ }
+ }
+ std::cerr << "QEF at: " << min_SNR << " SNR, speed: " << max_mbs << " Mb/s." << std::endl;
+ double QEF_SNR = design_SNR + 0.5;
+ assert(min_SNR < QEF_SNR);
+ std::cerr << "Polarization-Adjusted Convolutional list regression test passed!" << std::endl;
+ return 0;
+}
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