added polar code reliability sequence constructor

README.md

@@ -91,6 +91,12 @@ Bit freezers for the construction of [polar codes](https://en.wikipedia.org/wiki
 * PolarFreezer: Constructs code for a given erasure probability without the need for storing nor sorting of erasure probabilities for the virtual channels.
 * PolarCodeConst0: Constructs code by choosing the K best virtual channels computed from a given erasure probability.
 
+### [polar_sequence.hh](polar_sequence.hh)
+
+Construction of reliability sequences for [polar codes](https://en.wikipedia.org/wiki/Polar_code_(coding_theory)).
+
+* PolarSeqConst0: Constructs a sequence by sorting virtual channel reliabilities computed from a given erasure probability.
+
 ### [polar_encoder.hh](polar_encoder.hh)
 
 Encoders for [non-systematic and systematic](https://en.wikipedia.org/wiki/Systematic_code) [polar codes](https://en.wikipedia.org/wiki/Polar_code_(coding_theory)).

polar_sequence.hh

@@ -0,0 +1,40 @@
+/*
+Construct reliability sequences for polar codes
+
+Copyright 2023 Ahmet Inan <[email protected]>
+*/
+
+#pragma once
+
+#include <algorithm>
+
+namespace CODE {
+
+template <int MAX_M>
+class PolarSeqConst0
+{
+	void compute(double pe, int i, int h)
+	{
+		if (h) {
+			compute(pe * (2-pe), i, h/2);
+			compute(pe * pe, i+h, h/2);
+		} else {
+			prob[i] = pe;
+		}
+	}
+	double prob[1<<MAX_M];
+	int index[1<<MAX_M];
+public:
+	void operator()(int *sequence, int level, double erasure_probability = std::exp(-1.))
+	{
+		assert(level <= MAX_M);
+		int length = 1 << level;
+		compute(erasure_probability, 0, length / 2);
+		for (int i = 0; i < length; ++i)
+			sequence[i] = i;
+		std::sort(sequence, sequence+length, [this](int a, int b){ return prob[a] > prob[b]; });
+	}
+};
+
+}
+

tests/polar_list_regression_test.cc

@@ -15,7 +15,7 @@ Copyright 2020 Ahmet Inan <[email protected]>
 #include "polar_helper.hh"
 #include "polar_list_decoder.hh"
 #include "polar_encoder.hh"
-#include "polar_freezer.hh"
+#include "polar_sequence.hh"
 #include "crc.hh"
 #include "sequence.h"
 
@@ -52,35 +52,33 @@ int main()
 	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+31)/32];
+	auto frozen = new uint32_t[N/32];
 	auto codeword = new code_type[N];
 	auto temp = new simd_type[N];
 
-	long double erasure_probability = 0.5;
+	const int *reliability_sequence;
+	double erasure_probability = 0.5;
 	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
 	if (0) {
-		CODE::PolarFreezer freeze;
-		long double freezing_threshold = 0 ? 0.5 : std::numeric_limits<float>::epsilon();
-		K = freeze(frozen, M, erasure_probability, freezing_threshold);
-	} else {
-		auto freeze = new CODE::PolarCodeConst0<M>;
-		std::cerr << "sizeof(PolarCodeConst0<M>) = " << sizeof(CODE::PolarCodeConst0<M>) << std::endl;
+		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;
-		long double probability = std::exp(-pow(10.0, better_SNR / 10));
+		double probability = std::exp(-pow(10.0, better_SNR / 10));
 		std::cerr << "prob: " << probability << std::endl;
-		(*freeze)(frozen, M, K, probability);
-		delete freeze;
+		auto rel_seq = new int[N];
+		(*construct)(rel_seq, M, probability);
+		delete construct;
+		reliability_sequence = rel_seq;
+	} else {
+		reliability_sequence = sequence;
 	}
-#else
 	for (int i = 0; i < N / 32; ++i)
 		frozen[i] = 0;
 	for (int i = 0; i < N - K; ++i)
-		frozen[sequence[i]/32] |= 1 << (sequence[i]%32);
-#endif
+		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];

tests/polar_regression_test.cc

@@ -16,6 +16,7 @@ Copyright 2020 Ahmet Inan <[email protected]>
 #include "polar_decoder.hh"
 #include "polar_encoder.hh"
 #include "polar_freezer.hh"
+#include "polar_sequence.hh"
 
 bool get_bit(const uint32_t *bits, int idx)
 {
@@ -39,26 +40,33 @@ int main()
 	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+31)/32];
+	auto frozen = new uint32_t[N/32];
 	auto codeword = new code_type[N];
 	auto temp = new code_type[N];
 
-	long double erasure_probability = 1. / 3.;
+	double erasure_probability = 1. / 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) {
-		CODE::PolarFreezer freeze;
-		long double freezing_threshold = 0 ? 0.5 : std::numeric_limits<float>::epsilon();
-		K = freeze(frozen, M, erasure_probability, freezing_threshold);
-	} else {
+	double better_SNR = design_SNR + 0.5;//1.59175;
+	std::cerr << "better SNR: " << better_SNR << std::endl;
+	double probability = std::exp(-pow(10.0, better_SNR / 10));
+	if (1) {
 		auto freeze = new CODE::PolarCodeConst0<M>;
 		std::cerr << "sizeof(PolarCodeConst0<M>) = " << sizeof(CODE::PolarCodeConst0<M>) << std::endl;
-		double better_SNR = design_SNR + 0.5;//1.59175;
-		std::cerr << "better SNR: " << better_SNR << std::endl;
-		long double probability = std::exp(-pow(10.0, better_SNR / 10));
 		(*freeze)(frozen, M, K, probability);
 		delete freeze;
+	} else {
+		auto sequence = new int[N];
+		auto construct = new CODE::PolarSeqConst0<M>;
+		std::cerr << "sizeof(PolarSeqConst0<M>) = " << sizeof(CODE::PolarSeqConst0<M>) << std::endl;
+		(*construct)(sequence, M, probability);
+		delete construct;
+		for (int i = 0; i < N / 32; ++i)
+			frozen[i] = 0;
+		for (int i = 0; i < N - K; ++i)
+			frozen[sequence[i]/32] |= 1 << (sequence[i]%32);
+		delete[] sequence;
 	}
 	std::cerr << "Polar(" << N << ", " << K << ")" << std::endl;
 	auto message = new code_type[K];