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/* Reed-Solomon decoder
* Copyright 2002 Phil Karn, KA9Q
* May be used under the terms of the GNU General Public License (GPL)
*/
#ifdef DEBUG
#include <stdio.h>
#endif
#include <string.h>
#define NULL ((void *)0)
#define min(a,b) ((a) < (b) ? (a) : (b))
#ifdef FIXED
#include "fixed.h"
#elif defined(BIGSYM)
#include "int.h"
#else
#include "char.h"
#endif
int DECODE_RS(
#ifndef FIXED
void *p,
#endif
DTYPE *data, int *eras_pos, int no_eras){
#ifndef FIXED
struct rs *rs = (struct rs *)p;
#endif
int deg_lambda, el, deg_omega;
int i, j, r,k;
DTYPE u,q,tmp,num1,num2,den,discr_r;
DTYPE lambda[NROOTS+1], s[NROOTS]; /* Err+Eras Locator poly
* and syndrome poly */
DTYPE b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1];
DTYPE root[NROOTS], reg[NROOTS+1], loc[NROOTS];
int syn_error, count;
/* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
for(i=0;i<NROOTS;i++)
s[i] = data[0];
for(j=1;j<NN;j++){
for(i=0;i<NROOTS;i++){
if(s[i] == 0){
s[i] = data[j];
} else {
s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR+i)*PRIM)];
}
}
}
/* Convert syndromes to index form, checking for nonzero condition */
syn_error = 0;
for(i=0;i<NROOTS;i++){
syn_error |= s[i];
s[i] = INDEX_OF[s[i]];
}
if (!syn_error) {
/* if syndrome is zero, data[] is a codeword and there are no
* errors to correct. So return data[] unmodified
*/
count = 0;
goto finish;
}
memset(&lambda[1],0,NROOTS*sizeof(lambda[0]));
lambda[0] = 1;
if (no_eras > 0) {
/* Init lambda to be the erasure locator polynomial */
lambda[1] = ALPHA_TO[MODNN(PRIM*(NN-1-eras_pos[0]))];
for (i = 1; i < no_eras; i++) {
u = MODNN(PRIM*(NN-1-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)];
}
}
#if DEBUG >= 1
/* Test code that verifies the erasure locator polynomial just constructed
Needed only for decoder debugging. */
/* 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,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
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 != 0)
continue;
/* store root and error location number indices */
root[count] = i;
loc[count] = k;
count++;
}
if (count != no_eras) {
printf("count = %d no_eras = %d\n lambda(x) is WRONG\n",count,no_eras);
count = -1;
goto finish;
}
#if DEBUG >= 2
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<NROOTS+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 <= NROOTS) { /* 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-1] != A0)) {
discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r-i-1])];
}
}
discr_r = INDEX_OF[discr_r]; /* Index form */
if (discr_r == A0) {
/* 2 lines below: B(x) <-- x*B(x) */
memmove(&b[1],b,NROOTS*sizeof(b[0]));
b[0] = A0;
} else {
/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
t[0] = lambda[0];
for (i = 0 ; i < NROOTS; 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 <= NROOTS; i++)
b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
} else {
/* 2 lines below: B(x) <-- x*B(x) */
memmove(&b[1],b,NROOTS*sizeof(b[0]));
b[0] = A0;
}
memcpy(lambda,t,(NROOTS+1)*sizeof(t[0]));
}
}
/* Convert lambda to index form and compute deg(lambda(x)) */
deg_lambda = 0;
for(i=0;i<NROOTS+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 */
memcpy(®[1],&lambda[1],NROOTS*sizeof(reg[0]));
count = 0; /* Number of roots of lambda(x) */
for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
q = 1; /* lambda[0] is always 0 */
for (j = deg_lambda; j > 0; j--){
if (reg[j] != A0) {
reg[j] = MODNN(reg[j] + j);
q ^= ALPHA_TO[reg[j]];
}
}
if (q != 0)
continue; /* Not a root */
/* store root (index-form) and error location number */
#if DEBUG>=2
printf("count %d root %d loc %d\n",count,i,k);
#endif
root[count] = i;
loc[count] = k;
/* If we've already found max possible roots,
* abort the search to save time
*/
if(++count == deg_lambda)
break;
}
if (deg_lambda != count) {
/*
* deg(lambda) unequal to number of roots => uncorrectable
* error detected
*/
count = -1;
goto finish;
}
/*
* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
* x**NROOTS). in index form. Also find deg(omega).
*/
deg_omega = 0;
for (i = 0; i < NROOTS;i++){
tmp = 0;
j = (deg_lambda < i) ? deg_lambda : i;
for(;j >= 0; j--){
if ((s[i - j] != A0) && (lambda[j] != A0))
tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
}
if(tmp != 0)
deg_omega = i;
omega[i] = INDEX_OF[tmp];
}
omega[NROOTS] = A0;
/*
* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
* inv(X(l))**(FCR-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] * (FCR - 1) + NN)];
den = 0;
/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
for (i = min(deg_lambda,NROOTS-1) & ~1; i >= 0; i -=2) {
if(lambda[i+1] != A0)
den ^= ALPHA_TO[MODNN(lambda[i+1] + i * root[j])];
}
if (den == 0) {
#if DEBUG >= 1
printf("\n ERROR: denominator = 0\n");
#endif
count = -1;
goto finish;
}
/* Apply error to data */
if (num1 != 0) {
data[loc[j]] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])];
}
}
finish:
if(eras_pos != NULL){
for(i=0;i<count;i++)
eras_pos[i] = loc[i];
}
return count;
}
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