Schifra Reed-Solomon Error Correcting Code Library

Description

This example will demonstrate using C++ how to instantiate a Reed-Solomon encoder and decoder, add the full amount of possible errors, correct the errors, and output the various pieces of relevant information. The Reed-Solomon code's properties are as follows:

Symbol size: 8-bits
Codeword length: 255
Number of data symbols: 223
Number of FEC symbols: 32
Finite Field: GF(2⁸)
Finite Field polynomial: x⁸ + x⁷ + x² + x + 1
Generator polynomial roots: 32
Generator polynomial field index: 120th element (32 consecutive roots)

Schifra Data Channel Diagram - Copyright Arash Partow

#include <cstddef>
#include <iostream>
#include <string>

#include "schifra_galois_field.hpp"
#include "schifra_galois_field_polynomial.hpp"
#include "schifra_sequential_root_generator_polynomial_creator.hpp"
#include "schifra_reed_solomon_encoder.hpp"
#include "schifra_reed_solomon_decoder.hpp"
#include "schifra_reed_solomon_block.hpp"
#include "schifra_error_processes.hpp"

int main()
{
   /* Finite Field Parameters */
   const std::size_t field_descriptor                =   8;
   const std::size_t generator_polynomial_index      = 120;
   const std::size_t generator_polynomial_root_count =  32;

   /* Reed Solomon Code Parameters */
   const std::size_t code_length = 255;
   const std::size_t fec_length  =  32;
   const std::size_t data_length = code_length - fec_length;

   /* Instantiate Finite Field and Generator Polynomials */
   const schifra::galois::field field
                                (
                                   field_descriptor,
                                   schifra::galois::primitive_polynomial_size06,
                                   schifra::galois::primitive_polynomial06
                                );

   schifra::galois::field_polynomial generator_polynomial(field);

   if (
        !schifra::make_sequential_root_generator_polynomial
        (
           field,
           generator_polynomial_index,
           generator_polynomial_root_count,
           generator_polynomial
        )
      )
   {
      std::cout << "Error - Failed to create sequential root generator!" << std::endl;
      return 1;
   }

   /* Instantiate Encoder and Decoder (Codec) */
   typedef schifra::reed_solomon::encoder<code_length,fec_length,data_length> encoder_t;
   typedef schifra::reed_solomon::decoder<code_length,fec_length,data_length> decoder_t;

   const encoder_t encoder(field, generator_polynomial);
   const decoder_t decoder(field, generator_polynomial_index);

   std::string message = "An expert is someone who knows more and more about less and "
                         "less until they know absolutely everything about nothing";

   /* Pad message with nulls up until the code-word length */
   message.resize(code_length, 0x00);

   /* Instantiate RS Block For Codec */
   schifra::reed_solomon::block<code_length,fec_length> block;

   /* Transform message into Reed-Solomon encoded codeword */
   if (!encoder.encode(message, block))
   {
      std::cout << "Error - Critical encoding failure!" << std::endl;
      return 1;
   }

   /* Add errors at every 3rd location starting at position zero */
   schifra::corrupt_message_all_errors00(block, 0, 3);

   if (!decoder.decode(block))
   {
      std::cout << "Error - Critical decoding failure!" << std::endl;
      return 1;
   }
   else if (!schifra::is_block_equivelent(block, message))
   {
      std::cout << "Error - Error correction failed!" << std::endl;
      return 1;
   }

   block.data_to_string(message);

   return 0;
}