pe_std_array.c

error correction code

// ------------------------------------------------------------------------
// File: pe_std_array.c
//
// Exact probability of error with standard array decoding of binary
// linear codes.
// ------------------------------------------------------------------------
// This program is complementary material for the book:
//
// R.H. Morelos-Zaragoza, The Art of Error Correcting Coding, Wiley, 2002.
//
// ISBN 0471 49581 6
//
// This and other programs are available at http://the-art-of-ecc.com
//
// You may use this program for academic and personal purposes only. 
// If this program is used to perform simulations whose results are 
// published in a journal or book, please refer to the book above.
//
// The use of this program in a commercial product requires explicit
// written permission from the author. The author is not responsible or 
// liable for damage or loss that may be caused by the use of this program. 
//
// Copyright (c) 2002. Robert H. Morelos-Zaragoza. All rights reserved.
// ------------------------------------------------------------------------
#include <stdio.h>
#include <math.h>

#define NMAX 1024          // Maximum code length 

main(argc,argv)
int argc;
char **argv;
{
  int n, k;
  int t;
  double a[NMAX+1];        // Weight distribution
  double p, Pc;
  double rate;
  int i;
  double nd, id;

  double fact(double a);
  double comb(double a, double b);
  double Q(double a);

  double init,final,inc,eb_no_db,es_no;
  double nk2, vol;

  char name1[80], name2[80];
  FILE *fp1,*fp2;

  if (argc != 8)
  {
    printf("Usage: %s n k t file_Pe    init_SNR  final_SNR  inc_SNR\n",
    argv[0]);
    exit(1);
  }
  sscanf(argv[1], "%d", &n);
  sscanf(argv[2], "%d", &k);
  sscanf(argv[3], "%d", &t);
  sscanf(argv[4], "%s", name1);
  sscanf(argv[5], "%lf", &init);
  sscanf(argv[6], "%lf", &final);
  sscanf(argv[7], "%lf", &inc);

  rate = (double) k / (double) n;

  fp1 = fopen(name1,"w");

  nd = (double) n;

  for (eb_no_db = init; eb_no_db<=final; eb_no_db+=inc)
    {
    es_no = pow(10.0,(eb_no_db/10.0));   // snr per bit 
    es_no = es_no*rate;                  // snr per symbol 

    p = Q(sqrt(2.0*es_no));              // Bit error probability BPSK
    Pc = 0.0;

    // Correctable error patterns of weight up to t
    for (i=0; i<=t; i++)
      {
      id = (double) i;
      Pc += comb(nd,id) * pow(p,id)*pow((1.0-p),(nd-id));
      }

    // Add correctable error patterns of weight t+1
    nk2 = 1.0;
    for (i=0; i<n-k; i++)
      nk2 *= 2.0;                        // This gives 2^{n-k}
    vol = 0.0;
    for (i=0; i<=t; i++)
      {
      id = (double) i;
      vol += comb(nd,id);
      }
    Pc += (nk2 - vol) * pow(p,(double)t+1.0)*pow((1.0-p),(nd-(double)t+1.0));

    fprintf(fp1,"%lf %e\n", eb_no_db, 1.0-Pc);
    }

}

double fact(double a)
{
double i,tot;
  
    tot = 1.0;
    for (i=a;i>0.001;i=i-1.0)
    {
        tot = tot * i;
    }
    return(tot);
}

double comb(double a,double b)
{
double z,tot;
 
    if (a<b)
       return(1.0);
    if (b > (a-b))
    {
       tot = 1.0/fact(a-b);
       for (z=a;z>b;z=z-1.0)
       {
          tot = tot * z;
       }
    }
    else
    {
       tot = 1.0/fact(b);
       for (z=a;z>a-b;z=z-1.0)
       {
          tot = tot * z;
       }
    }
    return(tot);
}


double Q(double a)
{
        double erfc( double x );
    return(0.5*erfc(a/sqrt(2.0)));
}