rs.c

RS(n,k)编解码程序

 * elements of Gg[], which was generated above. Codeword is   c(X) =
 * data(X)*X**(NN-KK)+ b(X)
 */
int
encode_rs(dtype data[KK], dtype bb[NN-KK])
{
	register int i, j;
	gf feedback;

	CLEAR(bb,NN-KK);
	for (i = KK - 1; i >= 0; i--) {
#if (MM != 8)
		if(data[i] > NN)
			return -1;      /* Illegal symbol */
#endif
		feedback = Index_of[data[i] ^ bb[NN - KK - 1]];
		if (feedback != A0) {   /* feedback term is non-zero */
			for (j = NN - KK - 1; j > 0; j--)
				if (Gg[j] != A0)
					bb[j] = bb[j - 1] ^ Alpha_to[modnn(Gg[j] + feedback)];
				else
					bb[j] = bb[j - 1];
			bb[0] = Alpha_to[modnn(Gg[0] + feedback)];
		} else {        /* feedback term is zero. encoder becomes a
				 * single-byte shifter */
			for (j = NN - KK - 1; j > 0; j--)
				bb[j] = bb[j - 1];
			bb[0] = 0;
		}
	}
	return 0;
}

/*
 * Performs ERRORS+ERASURES decoding of RS codes. If decoding is successful,
 * writes the codeword into data[] itself. Otherwise data[] is unaltered.
 *
 * Return number of symbols corrected, or -1 if codeword is illegal
 * or uncorrectable.
 * 
 * First "no_eras" erasures are declared by the calling program. Then, the
 * maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
 * If the number of channel errors is not greater than "t_after_eras" the
 * transmitted codeword will be recovered. Details of algorithm can be found
 * in R. Blahut's "Theory ... of Error-Correcting Codes".
 */
int
eras_dec_rs(dtype data[NN], int eras_pos[NN-KK], int no_eras)
{
	int deg_lambda, el, deg_omega;
	int i, j, r;
	gf u,q,tmp,num1,num2,den,discr_r;
	gf recd[NN];
	gf lambda[NN-KK + 1], s[NN-KK + 1];     /* Err+Eras Locator poly
						 * and syndrome poly */
	gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
	gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
	int syn_error, count;

	/* data[] is in polynomial form, copy and convert to index form */
	for (i = NN-1; i >= 0; i--){
#if (MM != 8)
		if(data[i] > NN)
			return -1;      /* Illegal symbol */
#endif
		recd[i] = Index_of[data[i]];
	}
	/* first form the syndromes; i.e., evaluate recd(x) at roots of g(x)
	 * namely @**(B0+i), i = 0, ... ,(NN-KK-1)
	 */
	syn_error = 0;
	for (i = 1; i <= NN-KK; i++) {
		tmp = 0;
		for (j = 0; j < NN; j++)
			if (recd[j] != A0)      /* recd[j] in index form */
				tmp ^= Alpha_to[modnn(recd[j] + (B0+i-1)*j)];
		syn_error |= tmp;       /* set flag if non-zero syndrome =>
					 * error */
		/* store syndrome in index form  */
		s[i] = Index_of[tmp];
	}
	if (!syn_error) {
		/*
		 * if syndrome is zero, data[] is a codeword and there are no
		 * errors to correct. So return data[] unmodified
		 */
		return 0;
	}
	CLEAR(&lambda[1],NN-KK);
	lambda[0] = 1;
	if (no_eras > 0) {
		/* Init lambda to be the erasure locator polynomial */
		lambda[1] = Alpha_to[eras_pos[0]];
		for (i = 1; i < no_eras; i++) {
			u = eras_pos[i];
			for (j = i+1; j > 0; j--) {
				tmp = Index_of[lambda[j - 1]];
				if(tmp != A0)
					lambda[j] ^= Alpha_to[modnn(u + tmp)];
			}
		}
#ifdef ERASURE_DEBUG
		/* find roots of the erasure location polynomial */
		for(i=1;i<=no_eras;i++)
			reg[i] = Index_of[lambda[i]];
		count = 0;
		for (i = 1; i <= NN; i++) {
			q = 1;
			for (j = 1; j <= no_eras; j++)
				if (reg[j] != A0) {
					reg[j] = modnn(reg[j] + j);
					q ^= Alpha_to[reg[j]];
				}
			if (!q) {
				/* store root and error location
				 * number indices
				 */
				root[count] = i;
				loc[count] = NN - i;
				count++;
			}
		}
		if (count != no_eras) {
			printf("\n lambda(x) is WRONG\n");
			return -1;
		}
#ifndef NO_PRINT
		printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
		for (i = 0; i < count; i++)
			printf("%d ", loc[i]);
		printf("\n");
#endif
#endif
	}
	for(i=0;i<NN-KK+1;i++)
		b[i] = Index_of[lambda[i]];

	/*
	 * Begin Berlekamp-Massey algorithm to determine error+erasure
	 * locator polynomial
	 */
	r = no_eras;
	el = no_eras;
	while (++r <= NN-KK) {  /* r is the step number */
		/* Compute discrepancy at the r-th step in poly-form */
		discr_r = 0;
		for (i = 0; i < r; i++){
			if ((lambda[i] != 0) && (s[r - i] != A0)) {
				discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
			}
		}
		discr_r = Index_of[discr_r];    /* Index form */
		if (discr_r == A0) {
			/* 2 lines below: B(x) <-- x*B(x) */
			COPYDOWN(&b[1],b,NN-KK);
			b[0] = A0;
		} else {
			/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
			t[0] = lambda[0];
			for (i = 0 ; i < NN-KK; i++) {
				if(b[i] != A0)
					t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
				else
					t[i+1] = lambda[i+1];
			}
			if (2 * el <= r + no_eras - 1) {
				el = r + no_eras - el;
				/*
				 * 2 lines below: B(x) <-- inv(discr_r) *
				 * lambda(x)
				 */
				for (i = 0; i <= NN-KK; i++)
					b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
			} else {
				/* 2 lines below: B(x) <-- x*B(x) */
				COPYDOWN(&b[1],b,NN-KK);
				b[0] = A0;
			}
			COPY(lambda,t,NN-KK+1);
		}
	}

	/* Convert lambda to index form and compute deg(lambda(x)) */
	deg_lambda = 0;
	for(i=0;i<NN-KK+1;i++){
		lambda[i] = Index_of[lambda[i]];
		if(lambda[i] != A0)
			deg_lambda = i;
	}
	/*
	 * Find roots of the error+erasure locator polynomial. By Chien
	 * Search
	 */
	COPY(&reg[1],&lambda[1],NN-KK);
	count = 0;              /* Number of roots of lambda(x) */
	for (i = 1; i <= NN; i++) {
		q = 1;
		for (j = deg_lambda; j > 0; j--)
			if (reg[j] != A0) {
				reg[j] = modnn(reg[j] + j);
				q ^= Alpha_to[reg[j]];
			}
		if (!q) {
			/* store root (index-form) and error location number */
			root[count] = i;
			loc[count] = NN - i;
			count++;
		}
	}

#ifdef DEBUG
	printf("\n Final error positions:\t");
	for (i = 0; i < count; i++)
		printf("%d ", loc[i]);
	printf("\n");
#endif
	if (deg_lambda != count) {
		/*
		 * deg(lambda) unequal to number of roots => uncorrectable
		 * error detected
		 */
		return -1;
	}
	/*
	 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
	 * x**(NN-KK)). in index form. Also find deg(omega).
	 */
	deg_omega = 0;
	for (i = 0; i < NN-KK;i++){
		tmp = 0;
		j = (deg_lambda < i) ? deg_lambda : i;
		for(;j >= 0; j--){
			if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
				tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
		}
		if(tmp != 0)
			deg_omega = i;
		omega[i] = Index_of[tmp];
	}
	omega[NN-KK] = A0;

	/*
	 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
	 * inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
	 */
	for (j = count-1; j >=0; j--) {
		num1 = 0;
		for (i = deg_omega; i >= 0; i--) {
			if (omega[i] != A0)
				num1  ^= Alpha_to[modnn(omega[i] + i * root[j])];
		}
		num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
		den = 0;

		/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
		for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
			if(lambda[i+1] != A0)
				den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
		}
		if (den == 0) {
#ifdef DEBUG
			printf("\n ERROR: denominator = 0\n");
#endif
			return -1;
		}
		/* Apply error to data */
		if (num1 != 0) {
			data[loc[j]] ^= Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
		}
	}
	return count;
}