mirror of
https://github.com/saitohirga/WSJT-X.git
synced 2024-11-08 18:16:02 -05:00
0875a12cad
git-svn-id: svn+ssh://svn.code.sf.net/p/wsjt/wsjt/branches/map65@2464 ab8295b8-cf94-4d9e-aec4-7959e3be5d79
264 lines
6.8 KiB
C
264 lines
6.8 KiB
C
/* 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(
|
|
#ifdef FIXED
|
|
DTYPE *data, int *eras_pos, int no_eras,int pad){
|
|
#else
|
|
void *p,DTYPE *data, int *eras_pos, int no_eras){
|
|
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;
|
|
|
|
#ifdef FIXED
|
|
/* Check pad parameter for validity */
|
|
if(pad < 0 || pad >= NN)
|
|
return -1;
|
|
#endif
|
|
|
|
/* 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-PAD;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++)
|
|
// printf("%d %d %d\n",i,lambda[i],INDEX_OF[lambda[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 = deg_lambda-1;
|
|
for (i = 0; i <= deg_omega;i++){
|
|
tmp = 0;
|
|
for(j=i;j >= 0; j--){
|
|
if ((s[i - j] != A0) && (lambda[j] != A0))
|
|
tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
|
|
}
|
|
omega[i] = INDEX_OF[tmp];
|
|
}
|
|
|
|
/*
|
|
* 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 DEBUG >= 1
|
|
if (den == 0) {
|
|
printf("\n ERROR: denominator = 0\n");
|
|
count = -1;
|
|
goto finish;
|
|
}
|
|
#endif
|
|
/* Apply error to data */
|
|
if (num1 != 0 && loc[j] >= PAD) {
|
|
data[loc[j]-PAD] ^= 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;
|
|
}
|