bch_4148_4096_9_v100.cpp

对512Bytes的数据纠正4bit

/*
 * File:    bch_4148_4096_9_v100.cpp
 * Title:   Encoder/decoder for binary BCH codes in C (Version 3.1)
 * Author:  Robert Morelos-Zaragoza
 * Date:    August 1994
 * Revised: June 13, 1997
 *
 * ===============  Encoder/Decoder for binary BCH codes in C =================
 *
 * Version 1:   Original program. The user provides the generator polynomial
 *              of the code (cumbersome!).
 * Version 2:   Computes the generator polynomial of the code.
 * Version 3:   No need to input the coefficients of a primitive polynomial of
 *              degree m, used to construct the Galois Field GF(2**m). The
 *              program now works for any binary BCH code of length such that:
 *              2**(m-1) - 1 < length <= 2**m - 1
 *
 * Note:        You may have to change the size of the arrays to make it work.
 *
 * The encoding and decoding methods used in this program are based on the
 * book "Error Control Coding: Fundamentals and Applications", by Lin and
 * Costello, Prentice Hall, 1983.
 *
 * Thanks to Patrick Boyle ([e-mail]) for his observation that 'bch2.c'
 * did not work for lengths other than 2**m-1 which led to this new version.
 * Portions of this program are from 'rs.c', a Reed-Solomon encoder/decoder
 * in C, written by Simon Rockliff ([e-mail]) on 21/9/89. The
 * previous version of the BCH encoder/decoder in C, 'bch2.c', was written by
 * Robert Morelos-Zaragoza ([e-mail]) on 5/19/92.
 *
 * NOTE:    
 *          The author is not responsible for any malfunctioning of
 *          this program, nor for any damage caused by it. Please include the
 *          original program along with these comments in any redistribution.
 *
 *  For more information, suggestions, or other ideas on implementing error
 *  correcting codes, please contact me at:
 *
 *                           Robert Morelos-Zaragoza
 *                           5120 Woodway, Suite 7036
 *                           Houston, Texas 77056
 *
 *                    email: [e-mail]
 *
 * COPYRIGHT NOTICE: This computer program is free for non-commercial purposes.
 * You may implement this program for any non-commercial application. You may 
 * also implement this program for commercial purposes, provided that you
 * obtain my written permission. Any modification of this program is covered
 * by this copyright.
 *
 * == Copyright (c) 1994-7,  Robert Morelos-Zaragoza. All rights reserved.  ==
 *
 * m = order of the Galois field GF(2**m) 
 * n = 2**m - 1 = size of the multiplicative group of GF(2**m)
 * length = length of the BCH code
 * t = error correcting capability (max. no. of errors the code corrects)
 * d = 2*t + 1 = designed min. distance = no. of consecutive roots of g(x) + 1
 * k = n - deg(g(x)) = dimension (no. of information bits/codeword) of the code
 * p[] = coefficients of a primitive polynomial used to generate GF(2**m)
 * g[] = coefficients of the generator polynomial, g(x)
 * alpha_to [] = log table of GF(2**m) 
 * index_of[] = antilog table of GF(2**m)
 * data[] = information bits = coefficients of data polynomial, i(x)
 * bb[] = coefficients of redundancy polynomial x^(length-k) i(x) modulo g(x)
 * numerr = number of errors 
 * errpos[] = error positions 
 * recd[] = coefficients of the received polynomial 
 * decerror = number of decoding errors (in _message_ positions) 
 *
 */

#include "stdafx.h"
#include <math.h>
#include <stdlib.h>
#include <stdio.h>

#define DIMENSION 13
#define GFSIZE 8191
#define MINPOLYNOMIAL {1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1}

#define INFOSIZE 4096
#define CORRECTCAPACITY 4
#define REDUNDANCYSIZE 52
#define CODESIZE (INFOSIZE+REDUNDANCYSIZE)

#define GENPOLYNOMIAL {1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1}


// code parameter.
int             m = DIMENSION, n = GFSIZE, k = INFOSIZE, length = CODESIZE;
int             p[DIMENSION+1] = MINPOLYNOMIAL;
int             t = CORRECTCAPACITY;
int             d = (2*CORRECTCAPACITY-1);
int             g[REDUNDANCYSIZE+1] = GENPOLYNOMIAL;

// GF(2**m)
int             alpha_to[GFSIZE+1], index_of[GFSIZE+1];

int             data[INFOSIZE];
int             bb[REDUNDANCYSIZE], recd[CODESIZE];


void generate_gf()
{
	register int    i, mask;

	mask = 1;
	alpha_to[m] = 0;
	for (i = 0; i < m; i++) {
		alpha_to[i] = mask;
		index_of[alpha_to[i]] = i;
		if (p[i] != 0)
			alpha_to[m] ^= mask;
		mask <<= 1;
	}
	index_of[alpha_to[m]] = m;
	mask >>= 1;
	for (i = m + 1; i < n; i++) {
		if (alpha_to[i - 1] >= mask)
		  alpha_to[i] = alpha_to[m] ^ ((alpha_to[i - 1] ^ mask) << 1);
		else
		  alpha_to[i] = alpha_to[i - 1] << 1;
		index_of[alpha_to[i]] = i;
	}
	index_of[0] = -1;
}



void encode_bch()
{
	register int    i, j;
	register int    feedback;

	for (i = 0; i < REDUNDANCYSIZE; i++)
		bb[i] = 0;
	for (i = k - 1; i >= 0; i--) {
		feedback = data[i] ^ bb[REDUNDANCYSIZE - 1];
		if (feedback != 0) {
			for (j = REDUNDANCYSIZE - 1; j > 0; j--)
				if (g[j] != 0)
					bb[j] = bb[j - 1] ^ feedback;
				else
					bb[j] = bb[j - 1];
			bb[0] = g[0] && feedback;
		} else {
			for (j = REDUNDANCYSIZE - 1; j > 0; j--)
				bb[j] = bb[j - 1];
			bb[0] = 0;
		}
	}
}


void 
decode_bch()
/*
 * Simon Rockliff's implementation of Berlekamp's algorithm.
 *
 * Assume we have received bits in recd[i], i=0..(n-1).
 *
 * Compute the 2*t syndromes by substituting alpha^i into rec(X) and
 * evaluating, storing the syndromes in s[i], i=1..2t (leave s[0] zero) .
 * Then we use the Berlekamp algorithm to find the error location polynomial
 * elp[i].
 *
 * If the degree of the elp is >t, then we cannot correct all the errors, and
 * we have detected an uncorrectable error pattern. We output the information
 * bits uncorrected.
 *
 * If the degree of elp is <=t, we substitute alpha^i , i=1..n into the elp
 * to get the roots, hence the inverse roots, the error location numbers.
 * This step is usually called "Chien's search".
 *
 * If the number of errors located is not equal the degree of the elp, then
 * the decoder assumes that there are more than t errors and cannot correct
 * them, only detect them. We output the information bits uncorrected.
 */
{
	register int    i, j, u, q, t2, count = 0, syn_error = 0;
	int             elp[10][8], d[10], l[10], u_lu[10], s[9];
	int             root[200], loc[200], err[8], reg[201];

	t2 = 2 * t;

	/* first form the syndromes */
	printf("S(x) = ");
	for (i = 1; i <= t2; i++) {
		s[i] = 0;
		for (j = 0; j < length; j++)
			if (recd[j] != 0)
				s[i] ^= alpha_to[(i * j) % n];
		if (s[i] != 0)
			syn_error = 1; /* set error flag if non-zero syndrome */
/*
 * Note:    If the code is used only for ERROR DETECTION, then
 *          exit program here indicating the presence of errors.
 */
		/* convert syndrome from polynomial form to index form  */
		s[i] = index_of[s[i]];
		printf("%3d ", s[i]);
	}
	printf("\n");

	if (syn_error) {	/* if there are errors, try to correct them */
		/*
		 * Compute the error location polynomial via the Berlekamp
		 * iterative algorithm. Following the terminology of Lin and
		 * Costello's book :   d[u] is the 'mu'th discrepancy, where
		 * u='mu'+1 and 'mu' (the Greek letter!) is the step number
		 * ranging from -1 to 2*t (see L&C),  l[u] is the degree of
		 * the elp at that step, and u_l[u] is the difference between
		 * the step number and the degree of the elp. 
		 */
		/* initialise table entries */
		d[0] = 0;			/* index form */
		d[1] = s[1];		/* index form */
		elp[0][0] = 0;		/* index form */
		elp[1][0] = 1;		/* polynomial form */
		for (i = 1; i < t2; i++) {
			elp[0][i] = -1;	/* index form */
			elp[1][i] = 0;	/* polynomial form */
		}
		l[0] = 0;
		l[1] = 0;
		u_lu[0] = -1;
		u_lu[1] = 0;
		u = 0;
 
		do {
			u++;
			if (d[u] == -1) {
				l[u + 1] = l[u];
				for (i = 0; i <= l[u]; i++) {
					elp[u + 1][i] = elp[u][i];
					elp[u][i] = index_of[elp[u][i]];
				}
			} else
				/*
				 * search for words with greatest u_lu[q] for
				 * which d[q]!=0 
				 */
			{
				q = u - 1;
				while ((d[q] == -1) && (q > 0))
					q--;
				/* have found first non-zero d[q]  */
				if (q > 0) {
				  j = q;
				  do {
				    j--;
				    if ((d[j] != -1) && (u_lu[q] < u_lu[j]))
				      q = j;
				  } while (j > 0);
				}
 
				/*
				 * have now found q such that d[u]!=0 and
				 * u_lu[q] is maximum 
				 */
				/* store degree of new elp polynomial */
				if (l[u] > l[q] + u - q)
					l[u + 1] = l[u];
				else
					l[u + 1] = l[q] + u - q;
 
				/* form new elp(x) */
				for (i = 0; i < t2; i++)
					elp[u + 1][i] = 0;
				for (i = 0; i <= l[q]; i++)
					if (elp[q][i] != -1)
						elp[u + 1][i + u - q] = 
                                   alpha_to[(d[u] + n - d[q] + elp[q][i]) % n];
				for (i = 0; i <= l[u]; i++) {
					elp[u + 1][i] ^= elp[u][i];
					elp[u][i] = index_of[elp[u][i]];
				}
			}
			u_lu[u + 1] = u - l[u + 1];
 
			/* form (u+1)th discrepancy */
			if (u < t2) {	
			/* no discrepancy computed on last iteration */
			  if (s[u + 1] != -1)
			    d[u + 1] = alpha_to[s[u + 1]];
			  else
			    d[u + 1] = 0;
			    for (i = 1; i <= l[u + 1]; i++)
			      if ((s[u + 1 - i] != -1) && (elp[u + 1][i] != 0))
			        d[u + 1] ^= alpha_to[(s[u + 1 - i] 
			                      + index_of[elp[u + 1][i]]) % n];
			  /* put d[u+1] into index form */
			  d[u + 1] = index_of[d[u + 1]];	
			}
		} while ((u < t2) && (l[u + 1] <= t));
 
		u++;
		if (l[u] <= t) {/* Can correct errors */
			/* put elp into index form */
			for (i = 0; i <= l[u]; i++)
				elp[u][i] = index_of[elp[u][i]];

			printf("sigma(x) = ");
			for (i = 0; i <= l[u]; i++)
				printf("%3d ", elp[u][i]);
			printf("\n");
			printf("Roots: ");

			/* Chien search: find roots of the error location polynomial */
			for (i = 1; i <= l[u]; i++)
				reg[i] = elp[u][i];
			count = 0;
			for (i = 1; i <= n; i++) {
				q = 1;
				for (j = 1; j <= l[u]; j++)
					if (reg[j] != -1) {
						reg[j] = (reg[j] + j) % n;
						q ^= alpha_to[reg[j]];
					}
				if (!q) {	/* store root and error
						 * location number indices */
					root[count] = i;
					loc[count] = n - i;
					count++;
					printf("%3d ", n - i);
				}
			}
			printf("\n");
			if (count == l[u])	
			/* no. roots = degree of elp hence <= t errors */
				for (i = 0; i < l[u]; i++)
					recd[loc[i]] ^= 1;
			else	/* elp has degree >t hence cannot solve */
				printf("Incomplete decoding: errors detected\n");
		}
	}
}



int main(int argc, char* argv[])
{
	int             i;
	FILE*           datafile;
	char            ch;
	int             numerr = 3;
	int             errpos[CODESIZE] = {55, 97, 3543};
	int             decerror = 0;

	generate_gf();          /* Construct the Galois Field GF(2**m) */

	// get data
	datafile = fopen("test_data_bin_512.txt", "r");
	if(datafile == NULL)
	{
		printf("open file test_data_bin_512.txt failed!\n");
		return 1;
	}
	for(i=0 ; (i<INFOSIZE)&&(feof(datafile)==0); i++)
	{
		while(feof(datafile)==0)
		{
			ch = fgetc(datafile);
			if((ch=='0')||(ch=='1'))
			{
				data[i] = ch-'0';
				break;
			}
		}
	}
	fclose(datafile);

	encode_bch();           /* encode data */

	/*
	 * recd[] are the coefficients of c(x) = x**(length-k)*data(x) + b(x)
	 */
	printf("c(x) = \n");
	for (i = 0; i < REDUNDANCYSIZE; i++)
	{
		recd[i] = bb[i];
		
		if (i && ((i % 64) == 0))
			printf("\n");
		printf("%1d", recd[i]);
	}
	printf("\n");
	for (i = 0; i < INFOSIZE; i++)
	{
		recd[i + REDUNDANCYSIZE] = data[i];
		
		if (i && ((i % 64) == 0))
			printf("\n");
		printf("%1d", recd[i + REDUNDANCYSIZE]);
	}
	printf("\n");

	// add in the errors.
	if (numerr)
		for (i = 0; i < numerr; i++)
			recd[errpos[i]] ^= 1;
	printf("r(x) = \n");
	for (i = 0; i < REDUNDANCYSIZE; i++)
	{
		if (i && ((i % 64) == 0))
			printf("\n");
		printf("%1d", recd[i]);
	}
	printf("\n");
	for (i = 0; i < INFOSIZE; i++)
	{
		if (i && ((i % 64) == 0))
			printf("\n");
		printf("%1d", recd[i + REDUNDANCYSIZE]);
	}
	printf("\n");

	decode_bch();             /* DECODE received codeword recv[] */

	/*
	 * DECODING ERRORS? we compare only the data portion
	 */
	for (i = length - k; i < length; i++)
	{
		if (data[i - length + k] != recd[i])
		{
			decerror++;
			printf("Dismatch positions %2d\n", i);
		}
	}
	if (decerror)
	   printf("There were %d decoding errors in message positions\n", decerror);
	else
	   printf("Succesful decoding\n");
	
	return 0;
}