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bose_chaudhuri_hocquenghem_encoder.hh
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bose_chaudhuri_hocquenghem_encoder.hh
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/*
Bose Chaudhuri Hocquenghem Encoder
Copyright 2018 Ahmet Inan <inan@aicodix.de>
*/
#pragma once
#include <initializer_list>
#include "bitman.hh"
namespace CODE {
template <int LEN, int MSG>
class BoseChaudhuriHocquenghemEncoder
{
public:
static const int N = LEN, K = MSG, NP = N - K;
static const int G = ((NP+1)+7)/8;
private:
uint8_t generator[G];
static constexpr uint8_t slb1(uint8_t *buf, int pos)
{
return (buf[pos]<<1) | (buf[pos+1]>>7);
}
public:
BoseChaudhuriHocquenghemEncoder(std::initializer_list<int> minimal_polynomials)
{
// $generator(x) = \prod_i(minpoly_i(x))$
int generator_degree = 1;
for (int i = 0; i < G; ++i)
generator[i] = 0;
set_be_bit(generator, NP, 1);
for (auto m: minimal_polynomials) {
assert(0 < m);
int m_degree = 0;
while (m>>m_degree)
++m_degree;
--m_degree;
assert(generator_degree + m_degree <= NP + 1);
for (int i = generator_degree; i >= 0; --i) {
if (!get_be_bit(generator, NP-i))
continue;
set_be_bit(generator, NP-i, m&1);
for (int j = 1; j <= m_degree; ++j)
xor_be_bit(generator, NP-(i+j), (m>>j)&1);
}
generator_degree += m_degree;
}
assert(generator_degree == NP + 1);
if (0) {
std::cerr << "generator =";
for (int i = 0; i <= NP; ++i)
std::cerr << " " << get_be_bit(generator, NP-i);
std::cerr << std::endl;
}
for (int i = 0; i < NP; ++i)
set_be_bit(generator, i, get_be_bit(generator, i+1));
set_be_bit(generator, NP, 0);
}
void operator()(const uint8_t *data, uint8_t *parity, int data_len = K)
{
assert(0 < data_len && data_len <= K);
// $code = data * x^{NP} + (data * x^{NP}) \mod{generator}$
for (int l = 0; l <= (NP-1)/8; ++l)
parity[l] = 0;
for (int i = 0; i < data_len; ++i) {
if (get_be_bit(data, i) != get_be_bit(parity, 0)) {
for (int l = 0; l < (NP-1)/8; ++l)
parity[l] = generator[l] ^ slb1(parity, l);
parity[(NP-1)/8] = generator[(NP-1)/8] ^ (parity[(NP-1)/8]<<1);
} else {
for (int l = 0; l < (NP-1)/8; ++l)
parity[l] = slb1(parity, l);
parity[(NP-1)/8] <<= 1;
}
}
}
};
template <int ROOTS, int FCR, int MSG, typename GF>
class BoseChaudhuriHocquenghemEncoderReference
{
public:
typedef typename GF::value_type value_type;
typedef typename GF::ValueType ValueType;
typedef typename GF::IndexType IndexType;
static const int NR = ROOTS;
static const int N = GF::N, K = MSG, NP = N - K;
private:
ValueType generator[NP+1];
public:
BoseChaudhuriHocquenghemEncoderReference(std::initializer_list<int> minimal_polynomials)
{
// $generator(x) = \prod_i(minpoly_i(x))$
int generator_degree = 1;
generator[0] = ValueType(1);
for (int i = 1; i <= NP; ++i)
generator[i] = ValueType(0);
for (auto m: minimal_polynomials) {
assert(0 < m && m < 1<<(GF::M+1));
int m_degree = GF::M;
while (!(m>>m_degree))
--m_degree;
assert(generator_degree + m_degree <= NP + 1);
for (int i = generator_degree; i >= 0; --i) {
if (!generator[i])
continue;
generator[i] = ValueType(m&1);
for (int j = 1; j <= m_degree; ++j)
generator[i+j] += ValueType((m>>j)&1);
}
generator_degree += m_degree;
}
assert(generator_degree == NP + 1);
if (0) {
IndexType root(FCR), pe(1);
for (int i = 0; i < NR; ++i) {
ValueType tmp(generator[NP]);
for (int j = 1; j <= NP; ++j)
tmp = fma(root, tmp, generator[NP-j]);
assert(!tmp);
root *= pe;
}
std::cerr << "generator =";
for (int i = 0; i <= NP; ++i)
std::cerr << " " << (int)generator[i];
std::cerr << std::endl;
}
}
void operator()(const ValueType *data, ValueType *parity, int data_len = K)
{
assert(0 < data_len && data_len <= K);
// $code = data * x^{NP} + (data * x^{NP}) \mod{generator}$
for (int i = 0; i < NP; ++i)
parity[i] = ValueType(0);
for (int i = 0; i < data_len; ++i) {
if (data[i] != parity[0]) {
for (int j = 1; j < NP; ++j)
parity[j-1] = generator[NP-j] + parity[j];
parity[NP-1] = generator[0];
} else {
for (int j = 1; j < NP; ++j)
parity[j-1] = parity[j];
parity[NP-1] = ValueType(0);
}
}
}
};
}