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added encoder and syndrome decoder for short BCH codes
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Ahmet Inan
parent
1b4899c66d
commit
5d944ca7a9
6 changed files with 258 additions and 0 deletions
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@ -52,6 +52,14 @@ Implemented are the following Encoders and Decoders:
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* [bose_chaudhuri_hocquenghem_encoder.hh](bose_chaudhuri_hocquenghem_encoder.hh)
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* [bose_chaudhuri_hocquenghem_decoder.hh](bose_chaudhuri_hocquenghem_decoder.hh)
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### [short_bch_code_encoder.hh](short_bch_code_encoder.hh)
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Encoder for short [BCH codes](https://en.wikipedia.org/wiki/BCH_code)
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### [short_bch_code_decoder.hh](short_bch_code_decoder.hh)
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[Syndrome decoder](https://en.wikipedia.org/wiki/Decoding_methods#Syndrome_decoding) for short [BCH codes](https://en.wikipedia.org/wiki/BCH_code)
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### [simplex_encoder.hh](simplex_encoder.hh)
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Encoder for [Simplex codes](https://en.wikipedia.org/wiki/Linear_code).
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56
short_bch_code_decoder.hh
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56
short_bch_code_decoder.hh
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@ -0,0 +1,56 @@
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/*
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Decoder for short BCH codes
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Copyright 2020 Ahmet Inan <inan@aicodix.de>
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*/
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#pragma once
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namespace CODE {
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template <int N, int K>
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class ShortBCHCodeDecoder
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{
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static const int P = N - K;
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static const int W = 1 << K;
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static const int R = 1 << P;
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int err[R];
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short par[W];
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static_assert(N < 8 * sizeof(err[0]), "codeword type not wide enough");
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static_assert(P < 8 * sizeof(par[0]), "parity type not wide enough");
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static int modgen(int inp, int gen)
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{
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for (int i = K-1; i >= 0; --i) {
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int tmp = inp >> (i+P);
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inp ^= (tmp & 1) * (gen << i);
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}
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return inp;
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}
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public:
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ShortBCHCodeDecoder(int generator, int T)
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{
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for (int i = 0; i < W; ++i)
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par[i] = modgen(i << P, generator);
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err[0] = 0;
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assert(T > 0 && T <= 4);
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for (int a = 1<<(N-1); T >= 1 && a; a >>= 1) {
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err[modgen(a, generator)] = a;
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for (int b = a >> 1; T >= 2 && b; b >>= 1) {
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err[modgen(a|b, generator)] = a|b;
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for (int c = b >> 1; T >= 3 && c; c >>= 1) {
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err[modgen(a|b|c, generator)] = a|b|c;
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for (int d = c >> 1; T >= 4 && d; d >>= 1) {
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err[modgen(a|b|c|d, generator)] = a|b|c|d;
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}
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}
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}
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}
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}
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int operator()(int inp)
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{
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return inp ^ err[(par[inp>>P] ^ inp) & (R-1)];
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}
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};
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}
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40
short_bch_code_encoder.hh
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40
short_bch_code_encoder.hh
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@ -0,0 +1,40 @@
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/*
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Encoder for short BCH codes
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Copyright 2020 Ahmet Inan <inan@aicodix.de>
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*/
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#pragma once
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namespace CODE {
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template <int N, int K>
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class ShortBCHCodeEncoder
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{
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static const int P = N - K;
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static const int W = 1 << K;
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short par[W];
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static_assert(N < 8 * sizeof(int), "codeword type not wide enough");
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static_assert(P < 8 * sizeof(par[0]), "parity type not wide enough");
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static int modgen(int inp, int gen)
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{
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for (int i = K-1; i >= 0; --i) {
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int tmp = inp >> (i+P);
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inp ^= (tmp & 1) * (gen << i);
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}
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return inp;
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}
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public:
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ShortBCHCodeEncoder(int generator)
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{
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for (int i = 0; i < W; ++i)
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par[i] = modgen(i << P, generator);
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}
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int operator()(int msg)
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{
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return (msg << P) | par[msg];
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}
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};
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}
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59
tests/short_bch_code_decoder_test.cc
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59
tests/short_bch_code_decoder_test.cc
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@ -0,0 +1,59 @@
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/*
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Test for the short BCH codes decoder
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Copyright 2020 Ahmet Inan <inan@aicodix.de>
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*/
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#include <cassert>
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#include <random>
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#include <iostream>
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#include <functional>
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#include "short_bch_code_decoder.hh"
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int main()
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{
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std::random_device rd;
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std::default_random_engine generator(rd());
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if (1) {
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// Perfect binary Golay code using x^11+x^9+x^7+x^6+x^5+x+1
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const int N = 23, K = 12, T = 3, POLY = 0b101011100011;
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CODE::ShortBCHCodeDecoder<N, K> decode(POLY, T);
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int target = 0b10101101101111011111001;
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int damaged = target;
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typedef std::uniform_int_distribution<int> distribution;
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auto epos = std::bind(distribution(0, N-1), generator);
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for (int i = 0; i < T; ++i)
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damaged ^= 1 << epos();
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int recovered = decode(damaged);
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assert(recovered == target);
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}
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if (1) {
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// Perfect binary Golay code using x^11+x^10+x^6+x^5+x^4+x^2+1
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const int N = 23, K = 12, T = 3, POLY = 0b110001110101;
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CODE::ShortBCHCodeDecoder<N, K> decode(POLY, T);
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int target = 0b10101101101100100010101;
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int damaged = target;
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typedef std::uniform_int_distribution<int> distribution;
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auto epos = std::bind(distribution(0, N-1), generator);
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for (int i = 0; i < T; ++i)
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damaged ^= 1 << epos();
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int recovered = decode(damaged);
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assert(recovered == target);
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}
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if (1) {
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// NASA INTRO BCH(15, 5) T=3
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const int N = 15, K = 5, T = 3, POLY = 0b10100110111;
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CODE::ShortBCHCodeDecoder<N, K> decode(POLY, T);
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int target = 0b110010001111010;
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int damaged = target;
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typedef std::uniform_int_distribution<int> distribution;
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auto epos = std::bind(distribution(0, N-1), generator);
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for (int i = 0; i < T; ++i)
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damaged ^= 1 << epos();
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int recovered = decode(damaged);
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assert(recovered == target);
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}
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std::cerr << "Short BCH code decoder test passed!" << std::endl;
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return 0;
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}
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40
tests/short_bch_code_encoder_test.cc
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40
tests/short_bch_code_encoder_test.cc
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/*
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Test for the short BCH codes encoder
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Copyright 2020 Ahmet Inan <inan@aicodix.de>
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*/
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#include <cassert>
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#include <iostream>
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#include "short_bch_code_encoder.hh"
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int main()
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{
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if (1) {
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// Perfect binary Golay code using x^11+x^9+x^7+x^6+x^5+x+1
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CODE::ShortBCHCodeEncoder<23, 12> encode(0b101011100011);
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int message = 0b101011011011;
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int target = 0b10101101101111011111001;
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int codeword = encode(message);
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assert(target == codeword);
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}
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if (1) {
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// Perfect binary Golay code using x^11+x^10+x^6+x^5+x^4+x^2+1
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CODE::ShortBCHCodeEncoder<23, 12> encode(0b110001110101);
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int message = 0b101011011011;
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int target = 0b10101101101100100010101;
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int codeword = encode(message);
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assert(target == codeword);
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}
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if (1) {
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// NASA INTRO BCH(15, 5) T=3
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CODE::ShortBCHCodeEncoder<15, 5> encode(0b10100110111);
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int message = 0b11001;
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int target = 0b110010001111010;
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int codeword = encode(message);
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assert(target == codeword);
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}
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std::cerr << "Short BCH code encoder test passed!" << std::endl;
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return 0;
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}
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55
tests/short_bch_code_regression_test.cc
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55
tests/short_bch_code_regression_test.cc
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/*
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Regression Test for the short BCH codes encoder and decoder
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Copyright 2020 Ahmet Inan <inan@aicodix.de>
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*/
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#include <cassert>
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#include <random>
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#include <iostream>
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#include <functional>
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#include "short_bch_code_decoder.hh"
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#include "short_bch_code_encoder.hh"
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template <int N, int K, int T, int POLY>
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void bch_test(int trials)
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{
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CODE::ShortBCHCodeEncoder<N, K> encode(POLY);
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CODE::ShortBCHCodeDecoder<N, K> decode(POLY, T);
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std::random_device rd;
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typedef std::default_random_engine generator;
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typedef std::uniform_int_distribution<int> distribution;
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auto data = std::bind(distribution(0, (1<<K)-1), generator(rd()));
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auto epos = std::bind(distribution(0, N-1), generator(rd()));
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while (--trials) {
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int message = data();
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int codeword = encode(message);
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assert((codeword>>(N-K)) == message);
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int decoded = decode(codeword);
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assert(decoded == codeword);
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int damaged = codeword;
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for (int i = 0; i < T; ++i)
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damaged ^= 1 << epos();
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int recovered = decode(damaged);
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assert(recovered == codeword);
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}
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}
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int main()
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{
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if (1) {
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// Perfect binary Golay code using x^11+x^9+x^7+x^6+x^5+x+1
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bch_test<23, 12, 3, 0b101011100011>(1000000);
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}
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if (1) {
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// Perfect binary Golay code using x^11+x^10+x^6+x^5+x^4+x^2+1
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bch_test<23, 12, 3, 0b110001110101>(1000000);
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}
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if (1) {
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// NASA INTRO BCH(15, 5) T=3
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bch_test<15, 5, 3, 0b10100110111>(1000000);
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}
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std::cerr << "Short BCH code regression test passed!" << std::endl;
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return 0;
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}
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