WSJT-X/libm65/decode_rs.c

/* Reed-Solomon decoder
 * Copyright 2002 Phil Karn, KA9Q
 * May be used under the terms of the GNU General Public License (GPL)
 * Modified by Steve Franke, K9AN, for use in a soft-symbol RS decoder
 */

#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, int calc_syn){
    
#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];	// Err+Eras Locator poly
    static DTYPE s[51];					 // 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;
    
    if( calc_syn ) {
        /* 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(&reg[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;
}