bch3.c

this is bch coder in C

 * by the generator polynomial g(x).
 */
{
	register int    i, j;
	register int    feedback;

	for (i = 0; i < length - k; i++)
		bb[i] = 0;
	for (i = k - 1; i >= 0; i--) {
		feedback = data[i] ^ bb[length - k - 1];
		if (feedback != 0) {
			for (j = length - k - 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 = length - k - 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[1026][1024], d[1026], l[1026], u_lu[1026], s[1025];
	int             root[200], loc[200], err[1024], 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");
		}
	}
}



main()
{
	int             i;

	read_p();               /* Read m */
	generate_gf();          /* Construct the Galois Field GF(2**m) */
	gen_poly();             /* Compute the generator polynomial of BCH code */

	/* Randomly generate DATA */
	seed = 131073;
	srandom(seed);
	for (i = 0; i < k; i++)
		data[i] = ( random() & 65536 ) >> 16;

	encode_bch();           /* encode data */

	/*
	 * recd[] are the coefficients of c(x) = x**(length-k)*data(x) + b(x)
	 */
	for (i = 0; i < length - k; i++)
		recd[i] = bb[i];
	for (i = 0; i < k; i++)
		recd[i + length - k] = data[i];
	printf("Code polynomial:\nc(x) = ");
	for (i = 0; i < length; i++) {
		printf("%1d", recd[i]);
		if (i && ((i % 50) == 0))
			printf("\n");
	}
	printf("\n");

	printf("Enter the number of errors:\n");
	scanf("%d", &numerr);	/* CHANNEL errors */
    printf("Enter error locations (integers between");
    printf(" 0 and %d): ", length-1);
	/*
	 * recd[] are the coefficients of r(x) = c(x) + e(x)
	 */
	for (i = 0; i < numerr; i++)
		scanf("%d", &errpos[i]);
	if (numerr)
		for (i = 0; i < numerr; i++)
			recd[errpos[i]] ^= 1;
	printf("r(x) = ");
	for (i = 0; i < length; i++) {
		printf("%1d", recd[i]);
		if (i && ((i % 50) == 0))
			printf("\n");
	}
	printf("\n");

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

	/*
	 * print out original and decoded data
	 */
	printf("Results:\n");
	printf("original data  = ");
	for (i = 0; i < k; i++) {
		printf("%1d", data[i]);
		if (i && ((i % 50) == 0))
			printf("\n");
	}
	printf("\nrecovered data = ");
	for (i = length - k; i < length; i++) {
		printf("%1d", recd[i]);
		if ((i-length+k) && (((i-length+k) % 50) == 0))
			printf("\n");
	}
	printf("\n");

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