SSB_HighSpeed_Modem/hsmodem/fec/schifra_reed_solomon_decoder.hpp

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2020-11-05 13:11:57 -05:00
/*
(**************************************************************************)
(* *)
(* Schifra *)
(* Reed-Solomon Error Correcting Code Library *)
(* *)
(* Release Version 0.0.1 *)
(* http://www.schifra.com *)
(* Copyright (c) 2000-2020 Arash Partow, All Rights Reserved. *)
(* *)
(* The Schifra Reed-Solomon error correcting code library and all its *)
(* components are supplied under the terms of the General Schifra License *)
(* agreement. The contents of the Schifra Reed-Solomon error correcting *)
(* code library and all its components may not be copied or disclosed *)
(* except in accordance with the terms of that agreement. *)
(* *)
(* URL: http://www.schifra.com/license.html *)
(* *)
(**************************************************************************)
*/
#ifndef INCLUDE_SCHIFRA_REED_SOLOMON_DECODER_HPP
#define INCLUDE_SCHIFRA_REED_SOLOMON_DECODER_HPP
#include "schifra_galois_field.hpp"
#include "schifra_galois_field_element.hpp"
#include "schifra_galois_field_polynomial.hpp"
#include "schifra_reed_solomon_block.hpp"
#include "schifra_ecc_traits.hpp"
namespace schifra
{
namespace reed_solomon
{
template <std::size_t code_length, std::size_t fec_length, std::size_t data_length = code_length - fec_length>
class decoder
{
public:
typedef traits::reed_solomon_triat<code_length,fec_length,data_length> trait;
typedef block<code_length,fec_length> block_type;
decoder(const galois::field& field, const unsigned int& gen_initial_index = 0)
: decoder_valid_(field.size() == code_length),
field_(field),
X_(galois::generate_X(field_)),
gen_initial_index_(gen_initial_index)
{
if (decoder_valid_)
{
//Note: code_length and field size can be used interchangeably
create_lookup_tables();
}
};
const galois::field& field() const
{
return field_;
}
bool decode(block_type& rsblock) const
{
std::vector<std::size_t> erasure_list;
return decode(rsblock,erasure_list);
}
bool decode(block_type& rsblock, const erasure_locations_t& erasure_list) const
{
if ((!decoder_valid_) || (erasure_list.size() > fec_length))
{
rsblock.errors_detected = 0;
rsblock.errors_corrected = 0;
rsblock.zero_numerators = 0;
rsblock.unrecoverable = true;
rsblock.error = block_type::e_decoder_error0;
return false;
}
galois::field_polynomial received(field_,code_length - 1);
load_message(received,rsblock);
galois::field_polynomial syndrome(field_);
if (compute_syndrome(received,syndrome) == 0)
{
rsblock.errors_detected = 0;
rsblock.errors_corrected = 0;
rsblock.zero_numerators = 0;
rsblock.unrecoverable = false;
return true;
}
galois::field_polynomial lambda(galois::field_element(field_,1));
erasure_locations_t erasure_locations;
if (!erasure_list.empty())
{
prepare_erasure_list(erasure_locations, erasure_list);
compute_gamma(lambda, erasure_locations);
}
if (erasure_list.size() < fec_length)
{
modified_berlekamp_massey_algorithm(lambda, syndrome, erasure_list.size());
}
std::vector<int> error_locations;
find_roots(lambda, error_locations);
if (0 == error_locations.size())
{
/*
Syndrome is non-zero yet no error locations have
been obtained, conclusion:
It is possible that there are MORE errrors in the
message than can be detected and corrected for this
particular code.
*/
rsblock.errors_detected = 0;
rsblock.errors_corrected = 0;
rsblock.zero_numerators = 0;
rsblock.unrecoverable = true;
rsblock.error = block_type::e_decoder_error1;
return false;
}
else if (((2 * error_locations.size()) - erasure_list.size()) > fec_length)
{
/*
Too many errors\erasures! 2E + S <= fec_length
L = E + S
E = L - S
2E = 2L - 2S
2E + S = 2L - 2S + S
= 2L - S
Where:
L : Error Locations
E : Errors
S : Erasures
*/
rsblock.errors_detected = error_locations.size();
rsblock.errors_corrected = 0;
rsblock.zero_numerators = 0;
rsblock.unrecoverable = true;
rsblock.error = block_type::e_decoder_error2;
return false;
}
else
rsblock.errors_detected = error_locations.size();
return forney_algorithm(error_locations, lambda, syndrome, rsblock);
}
private:
decoder();
decoder(const decoder& dec);
decoder& operator=(const decoder& dec);
protected:
void load_message(galois::field_polynomial& received, const block_type& rsblock) const
{
/*
Load message data into received polynomial in reverse order.
*/
for (std::size_t i = 0; i < code_length; ++i)
{
received[code_length - 1 - i] = rsblock[i];
}
}
void create_lookup_tables()
{
root_exponent_table_.reserve(field_.size() + 1);
for (int i = 0; i < static_cast<int>(field_.size() + 1); ++i)
{
root_exponent_table_.push_back(field_.exp(field_.alpha(code_length - i),(1 - gen_initial_index_)));
}
syndrome_exponent_table_.reserve(fec_length);
for (int i = 0; i < static_cast<int>(fec_length); ++i)
{
syndrome_exponent_table_.push_back(field_.alpha(gen_initial_index_ + i));
}
gamma_table_.reserve(field_.size() + 1);
for (int i = 0; i < static_cast<int>(field_.size() + 1); ++i)
{
gamma_table_.push_back((1 + (X_ * galois::field_element(field_,field_.alpha(i)))));
}
}
void prepare_erasure_list(erasure_locations_t& erasure_locations, const erasure_locations_t& erasure_list) const
{
/*
Note: 1. Erasure positions must be unique.
2. Erasure positions must exist within the code block.
There are NO exceptions to these rules!
*/
erasure_locations.resize(erasure_list.size());
for (std::size_t i = 0; i < erasure_list.size(); ++i)
{
erasure_locations[i] = (code_length - 1 - erasure_list[i]);
}
}
int compute_syndrome(const galois::field_polynomial& received,
galois::field_polynomial& syndrome) const
{
int error_flag = 0;
syndrome = galois::field_polynomial(field_,fec_length - 1);
for (std::size_t i = 0; i < fec_length; ++i)
{
syndrome[i] = received(syndrome_exponent_table_[i]);
error_flag |= syndrome[i].poly();
}
return error_flag;
}
void compute_gamma(galois::field_polynomial& gamma, const erasure_locations_t& erasure_locations) const
{
for (std::size_t i = 0; i < erasure_locations.size(); ++i)
{
gamma *= gamma_table_[erasure_locations[i]];
}
}
void find_roots(const galois::field_polynomial& poly, std::vector<int>& root_list) const
{
/*
Chien Search: Find the roots of the error locator polynomial
via an exhaustive search over all non-zero elements in the
given finite field.
*/
root_list.reserve(fec_length << 1);
root_list.resize(0);
const std::size_t polynomial_degree = poly.deg();
for (int i = 1; i <= static_cast<int>(code_length); ++i)
{
if (0 == poly(field_.alpha(i)).poly())
{
root_list.push_back(i);
if (polynomial_degree == root_list.size())
{
break;
}
}
}
}
void compute_discrepancy(galois::field_element& discrepancy,
const galois::field_polynomial& lambda,
const galois::field_polynomial& syndrome,
const std::size_t& l,
const std::size_t& round) const
{
/*
*
Compute the lambda discrepancy at the current round of BMA
min: if(a<b)?a:b
*/
// std::size_t upper_bound = std::min(static_cast<int>(l), lambda.deg());
// does not compile under Windows and has been replaced with:
std::size_t bb = lambda.deg();
std::size_t aa = static_cast<int>(l);
std::size_t upper_bound = 0;
if (aa < bb)
upper_bound = aa;
else
upper_bound = bb;
discrepancy = 0;
for (std::size_t i = 0; i <= upper_bound; ++i)
{
discrepancy += lambda[i] * syndrome[round - i];
}
}
void modified_berlekamp_massey_algorithm(galois::field_polynomial& lambda,
const galois::field_polynomial& syndrome,
const std::size_t erasure_count) const
{
/*
Modified Berlekamp-Massey Algorithm
Identify the shortest length linear feed-back shift register (LFSR)
that will generate the sequence equivalent to the syndrome.
*/
int i = -1;
std::size_t l = erasure_count;
galois::field_element discrepancy(field_,0);
galois::field_polynomial previous_lambda = lambda << 1;
for (std::size_t round = erasure_count; round < fec_length; ++round)
{
compute_discrepancy(discrepancy, lambda, syndrome, l, round);
if (discrepancy != 0)
{
galois::field_polynomial tau = lambda - (discrepancy * previous_lambda);
if (static_cast<int>(l) < (static_cast<int>(round) - i))
{
const std::size_t tmp = round - i;
i = static_cast<int>(round - l);
l = tmp;
previous_lambda = lambda / discrepancy;
}
lambda = tau;
}
previous_lambda <<= 1;
}
}
bool forney_algorithm(const std::vector<int>& error_locations,
const galois::field_polynomial& lambda,
const galois::field_polynomial& syndrome,
block_type& rsblock) const
{
/*
The Forney algorithm for computing the error magnitudes
*/
const galois::field_polynomial omega = (lambda * syndrome) % fec_length;
const galois::field_polynomial lambda_derivative = lambda.derivative();
rsblock.errors_corrected = 0;
rsblock.zero_numerators = 0;
for (std::size_t i = 0; i < error_locations.size(); ++i)
{
const unsigned int error_location = error_locations[i];
const galois::field_symbol alpha_inverse = field_.alpha(error_location);
const galois::field_symbol numerator = (omega(alpha_inverse) * root_exponent_table_[error_location]).poly();
const galois::field_symbol denominator = lambda_derivative(alpha_inverse).poly();
if (0 != numerator)
{
if (0 != denominator)
{
rsblock[error_location - 1] ^= field_.div(numerator, denominator);
rsblock.errors_corrected++;
}
else
{
rsblock.unrecoverable = true;
rsblock.error = block_type::e_decoder_error3;
return false;
}
}
else
++rsblock.zero_numerators;
}
if (lambda.deg() == static_cast<int>(rsblock.errors_detected))
return true;
else
{
rsblock.unrecoverable = true;
rsblock.error = block_type::e_decoder_error4;
return false;
}
}
protected:
bool decoder_valid_;
const galois::field& field_;
std::vector<galois::field_symbol> root_exponent_table_;
std::vector<galois::field_symbol> syndrome_exponent_table_;
std::vector<galois::field_polynomial> gamma_table_;
const galois::field_polynomial X_;
const unsigned int gen_initial_index_;
};
template <std::size_t code_length,
std::size_t fec_length,
std::size_t data_length = code_length - fec_length,
std::size_t natural_length = 255, // Needs to be in-sync with field size
std::size_t padding_length = natural_length - data_length - fec_length>
class shortened_decoder
{
public:
typedef traits::reed_solomon_triat<code_length,fec_length,data_length> trait;
typedef block<code_length,fec_length> block_type;
shortened_decoder(const galois::field& field, const unsigned int gen_initial_index = 0)
: decoder_(field, gen_initial_index)
{}
inline bool decode(block_type& rsblock, const erasure_locations_t& erasure_list) const
{
typename natural_decoder_type::block_type block;
std::fill_n(&block[0], padding_length, typename block_type::symbol_type(0));
for (std::size_t i = 0; i < code_length; ++i)
{
block.data[padding_length + i] = rsblock.data[i];
}
erasure_locations_t shifted_position_erasure_list(erasure_list.size(),0);
for (std::size_t i = 0; i < erasure_list.size(); ++i)
{
shifted_position_erasure_list[i] = erasure_list[i] + padding_length;
}
if (decoder_.decode(block, shifted_position_erasure_list))
{
for (std::size_t i = 0; i < code_length; ++i)
{
rsblock.data[i] = block.data[padding_length + i];
}
rsblock.copy_state(block);
return true;
}
else
{
rsblock.copy_state(block);
return false;
}
}
inline bool decode(block_type& rsblock) const
{
typename natural_decoder_type::block_type block;
std::fill_n(&block[0], padding_length, typename block_type::symbol_type(0));
for (std::size_t i = 0; i < code_length; ++i)
{
block.data[padding_length + i] = rsblock.data[i];
}
if (decoder_.decode(block))
{
for (std::size_t i = 0; i < code_length; ++i)
{
rsblock.data[i] = block.data[padding_length + i];
}
rsblock.copy_state(block);
return true;
}
else
{
rsblock.copy_state(block);
return false;
}
}
private:
typedef decoder<natural_length,fec_length> natural_decoder_type;
const natural_decoder_type decoder_;
};
} // namespace reed_solomon
} // namespace schifra
#endif