bch_awgn.c

The intention is to show you how to incorporate the AWGN/Rayleigh fading models in the basic decodin

	for (ii = 1; ii <= nocycles; ii++) {
		min[kaux] = 0;
		test = 0;
		for (jj = 0; ((jj < size[ii]) && (!test)); jj++)
			for (root = 1; ((root < d) && (!test)); root++)
				if (root == cycle[ii][jj])  {
					test = 1;
					min[kaux] = ii;
				}
		if (min[kaux]) {
			rdncy += size[min[kaux]];
			kaux++;
		}
	}
	noterms = kaux;
	kaux = 1;
	for (ii = 0; ii < noterms; ii++)
		for (jj = 0; jj < size[min[ii]]; jj++) {
			zeros[kaux] = cycle[min[ii]][jj];
			kaux++;
		}

	k = length - rdncy;

    if (k<0)
      {
         printf("Parameters invalid!\n");
         exit(0);
      }

	printf("This is a (%d, %d, %d) binary BCH code\n", length, k, d);

	/* Compute the generator polynomial */
	g[0] = alpha_to[zeros[1]];
	g[1] = 1;		/* g(x) = (X + zeros[1]) initially */
	for (ii = 2; ii <= rdncy; ii++) {
	  g[ii] = 1;
	  for (jj = ii - 1; jj > 0; jj--)
	    if (g[jj] != 0)
	      g[jj] = g[jj - 1] ^ alpha_to[(index_of[g[jj]] + zeros[ii]) % n];
	    else
	      g[jj] = g[jj - 1];
	  g[0] = alpha_to[(index_of[g[0]] + zeros[ii]) % n];
	}
	printf("Generator polynomial:\ng(x) = ");
	for (ii = 0; ii <= rdncy; ii++) {
	  printf("%d", g[ii]);
	  if (ii && ((ii % 50) == 0))
	    printf("\n");
	}
	printf("\n");
}


void 
encode_bch()
/*
 * Compute redundacy bb[], the coefficients of b(x). The redundancy
 * polynomial b(x) is the remainder after dividing x^(length-k)*data(x)
 * 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 */
	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]];
	}

	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]];

			/* 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++;
				}
			}
			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 */
		}
	}
}



void bpsk_awgn()
//
// BPSK map, AWGN add and BPSK detect
// 
{
  	double u1,u2,s,noise,randmum;
  	double trans[1024];
  	int i;

  	for (i=0; i<n; i++)
    	{
      		if (recd[i]) trans[i] = -1.0; else trans[i] = 1.0;
      		do {
            		randmum = (double)(random())/MAX_RANDOM;
            		u1 = randmum*2.0 - 1.0;
            		randmum = (double)(random())/MAX_RANDOM;
            		u2 = randmum*2.0 - 1.0;
            		s = u1*u1 + u2*u2;
            	} while( s >= 1);
      		noise = u1 * sqrt( (-2.0*log(s))/s );
      		trans[i] += noise/amp;
      		if (trans[i]<0.0) recd[i] = 1; else recd[i] = 0;
    	}
}