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Simulation of a Reed-Solomon Block Code

A Reed-Solomon code is a $q^m$-ary BCH code of length $q^m-1$. The generator polynomial for a $t$-error correcting code is $g(x) = (x-\alpha) (x-\alpha^1) \ldots (x-\alpha^{2t-1})$. The decoder uses the Berlkamp-Massey algorithm for decoding as described in: S. B. Wicker, "Error Control Systems for digital communication and storage," Prentice Hall. The following example simulates a binary (i.e. $q=2$) Reed-Solomon code with parameters $m$ and $t$:

#include <itpp/itcomm.h>
using namespace itpp;
//These lines are needed for use of cout and endl
using std::cout;
using std::endl;
int main()
{
//Scalars and vectors:
int m, t, n, k, q, NumBits, NumCodeWords;
double p;
//Set parameters:
NumCodeWords = 1000; //Number of Reed-Solomon code-words to simulate
p = 0.01; //BSC Error probability
m = 3; //Reed-Solomon parameter m
t = 2; //Reed-Solomon parameter t
cout << "Number of Reed-Solomon code-words to simulate: " << NumCodeWords << endl;
cout << "BSC Error probability : " << p << endl;
cout << "RS m: " << m << endl;
cout << "RS t: " << t << endl;
//Classes:
BSC bsc(p);
RNG_randomize();
//Calculate parameters for the Reed-Solomon Code:
n = round_i(pow(2.0, m) - 1);
k = round_i(pow(2.0, m)) - 1 - 2 * t;
q = round_i(pow(2.0, m));
cout << "Simulating an Reed-Solomon code with the following parameters:" << endl;
cout << "n = " << n << endl;
cout << "k = " << k << endl;
cout << "q = " << q << endl;
NumBits = m * k * NumCodeWords;
cout << "The bit error probability after decoding is " << berc.get_errorrate() << endl;
//Exit program:
return 0;
}
General array class.
Definition array.h:105
Bit Error Rate Counter (BERC) Class.
A Binary Symetric Channel with crossover probability p.
Definition channel.h:1038
Reed-Solomon Codes.
Definition reedsolomon.h:52
Include file for the IT++ communications module.
itpp namespace
Definition itmex.h:37

A typical run of this program can look like this:

Number of Reed-Solomon code-words to simulate: 1000
BSC Error probability : 0.01
RS m: 3
RS t: 2
Simulating an Reed-Solomon code with the following parameters:
n = 7
k = 3
q = 8
The bit error probability after decoding is 0.000333333
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