Add modified versions of Karn RS routines.

This commit is contained in:
Joe Taylor 2024-02-01 08:52:46 -05:00
parent c228340519
commit 0cf544e3aa
6 changed files with 589 additions and 0 deletions

263
lib/superfox/decode_rs.c Normal file
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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_sf.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(&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 = 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;
}

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lib/superfox/encode_rs.c Normal file
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/* Reed-Solomon encoder
* Copyright 2002, Phil Karn, KA9Q
* May be used under the terms of the GNU General Public License (GPL)
*/
#include <string.h>
#ifdef FIXED
#include "fixed.h"
#elif defined(BIGSYM)
#include "int_sf.h"
#else
#include "char.h"
#endif
void ENCODE_RS(
#ifdef FIXED
DTYPE *data, DTYPE *bb,int pad){
#else
void *p,DTYPE *data, DTYPE *bb){
struct rs *rs = (struct rs *)p;
#endif
int i, j;
DTYPE feedback;
#ifdef FIXED
/* Check pad parameter for validity */
if(pad < 0 || pad >= NN)
return;
#endif
memset(bb,0,NROOTS*sizeof(DTYPE));
for(i=0;i<NN-NROOTS-PAD;i++){
feedback = INDEX_OF[data[i] ^ bb[0]];
if(feedback != A0){ /* feedback term is non-zero */
#ifdef UNNORMALIZED
/* This line is unnecessary when GENPOLY[NROOTS] is unity, as it must
* always be for the polynomials constructed by init_rs()
*/
feedback = MODNN(NN - GENPOLY[NROOTS] + feedback);
#endif
for(j=1;j<NROOTS;j++)
bb[j] ^= ALPHA_TO[MODNN(feedback + GENPOLY[NROOTS-j])];
}
/* Shift */
memmove(&bb[0],&bb[1],sizeof(DTYPE)*(NROOTS-1));
if(feedback != A0)
bb[NROOTS-1] = ALPHA_TO[MODNN(feedback + GENPOLY[0])];
else
bb[NROOTS-1] = 0;
}
}

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lib/superfox/init_rs.c Normal file
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/* Initialize a RS codec
*
* Copyright 2002 Phil Karn, KA9Q
* May be used under the terms of the GNU General Public License (GPL)
*/
#include <stdlib.h>
#ifdef CCSDS
#include "ccsds.h"
#elif defined(BIGSYM)
#include "int_sf.h"
#else
#include "char.h"
#endif
#define NULL ((void *)0)
void FREE_RS(void *p){
struct rs *rs = (struct rs *)p;
free(rs->alpha_to);
free(rs->index_of);
free(rs->genpoly);
free(rs);
}
/* Initialize a Reed-Solomon codec
* symsize = symbol size, bits (1-8)
* gfpoly = Field generator polynomial coefficients
* fcr = first root of RS code generator polynomial, index form
* prim = primitive element to generate polynomial roots
* nroots = RS code generator polynomial degree (number of roots)
* pad = padding bytes at front of shortened block
*/
void *INIT_RS(int symsize,int gfpoly,int fcr,int prim,
int nroots,int pad){
struct rs *rs;
int i, j, sr,root,iprim;
/* Check parameter ranges */
if(symsize < 0 || symsize > 8*sizeof(DTYPE))
return NULL; /* Need version with ints rather than chars */
if(fcr < 0 || fcr >= (1<<symsize))
return NULL;
if(prim <= 0 || prim >= (1<<symsize))
return NULL;
if(nroots < 0 || nroots >= (1<<symsize))
return NULL; /* Can't have more roots than symbol values! */
if(pad < 0 || pad >= ((1<<symsize) -1 - nroots))
return NULL; /* Too much padding */
rs = (struct rs *)calloc(1,sizeof(struct rs));
rs->mm = symsize;
rs->nn = (1<<symsize)-1;
rs->pad = pad;
rs->alpha_to = (DTYPE *)malloc(sizeof(DTYPE)*(rs->nn+1));
if(rs->alpha_to == NULL){
free(rs);
return NULL;
}
rs->index_of = (DTYPE *)malloc(sizeof(DTYPE)*(rs->nn+1));
if(rs->index_of == NULL){
free(rs->alpha_to);
free(rs);
return NULL;
}
/* Generate Galois field lookup tables */
rs->index_of[0] = A0; /* log(zero) = -inf */
rs->alpha_to[A0] = 0; /* alpha**-inf = 0 */
sr = 1;
for(i=0;i<rs->nn;i++){
rs->index_of[sr] = i;
rs->alpha_to[i] = sr;
sr <<= 1;
if(sr & (1<<symsize))
sr ^= gfpoly;
sr &= rs->nn;
}
if(sr != 1){
/* field generator polynomial is not primitive! */
free(rs->alpha_to);
free(rs->index_of);
free(rs);
return NULL;
}
/* Form RS code generator polynomial from its roots */
rs->genpoly = (DTYPE *)malloc(sizeof(DTYPE)*(nroots+1));
if(rs->genpoly == NULL){
free(rs->alpha_to);
free(rs->index_of);
free(rs);
return NULL;
}
rs->fcr = fcr;
rs->prim = prim;
rs->nroots = nroots;
/* Find prim-th root of 1, used in decoding */
for(iprim=1;(iprim % prim) != 0;iprim += rs->nn)
;
rs->iprim = iprim / prim;
rs->genpoly[0] = 1;
for (i = 0,root=fcr*prim; i < nroots; i++,root += prim) {
rs->genpoly[i+1] = 1;
/* Multiply rs->genpoly[] by @**(root + x) */
for (j = i; j > 0; j--){
if (rs->genpoly[j] != 0)
rs->genpoly[j] = rs->genpoly[j-1] ^ rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[j]] + root)];
else
rs->genpoly[j] = rs->genpoly[j-1];
}
/* rs->genpoly[0] can never be zero */
rs->genpoly[0] = rs->alpha_to[modnn(rs,rs->index_of[rs->genpoly[0]] + root)];
}
/* convert rs->genpoly[] to index form for quicker encoding */
for (i = 0; i <= nroots; i++)
rs->genpoly[i] = rs->index_of[rs->genpoly[i]];
return rs;
}

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/* Include file to configure the RS codec for integer symbols
*
* Copyright 2002, Phil Karn, KA9Q
* May be used under the terms of the GNU General Public License (GPL)
*/
#define DTYPE int
/* Reed-Solomon codec control block */
struct rs {
int mm; /* Bits per symbol */
int nn; /* Symbols per block (= (1<<mm)-1) */
DTYPE *alpha_to; /* log lookup table */
DTYPE *index_of; /* Antilog lookup table */
DTYPE *genpoly; /* Generator polynomial */
int nroots; /* Number of generator roots = number of parity symbols */
int fcr; /* First consecutive root, index form */
int prim; /* Primitive element, index form */
int iprim; /* prim-th root of 1, index form */
int pad; /* Padding bytes in shortened block */
};
static inline int modnn(struct rs *rs,int x){
while (x >= rs->nn) {
x -= rs->nn;
x = (x >> rs->mm) + (x & rs->nn);
}
return x;
}
#define MODNN(x) modnn(rs,x)
#define MM (rs->mm)
#define NN (rs->nn)
#define ALPHA_TO (rs->alpha_to)
#define INDEX_OF (rs->index_of)
#define GENPOLY (rs->genpoly)
#define NROOTS (rs->nroots)
#define FCR (rs->fcr)
#define PRIM (rs->prim)
#define IPRIM (rs->iprim)
#define PAD (rs->pad)
#define A0 (NN)
#define ENCODE_RS encode_rs_sf
#define DECODE_RS decode_rs_sf
#define INIT_RS init_rs_sf
#define FREE_RS free_rs_sf
void ENCODE_RS(void *p,DTYPE *data,DTYPE *parity);
int DECODE_RS(void *p,DTYPE *data,int *eras_pos,int no_eras);
void *INIT_RS(int symsize,int gfpoly,int fcr,
int prim,int nroots,int pad);
void FREE_RS(void *p);

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#include <stdio.h>
#include "rs_sf.h"
void *rs;
static int first=1;
static int nn,kk,nroots,npad;
void rs_init_(int *mm, int *nq, int *nn0, int *kk0, int *nfz)
{
nn=*nn0;
kk=*kk0;
nroots=nn-kk;
npad=*nq-1-nn;
if(*mm==6) rs=init_rs_sf(*mm,0x43,*nfz,1,nroots,npad); //M=6
if(*mm==7) rs=init_rs_sf(*mm,0x89,*nfz,1,nroots,npad); //M=7
if(*mm==8) rs=init_rs_sf(*mm,0x11d,*nfz,1,nroots,npad); //M=8
first=0;
}
void rs_encode_(int *dgen, int *sent)
// Encode JT65 data dgen[...], producing sent[...].
{
int dat1[256];
int b[256];
int i;
// Reverse data order for the Karn codec.
for(i=0; i<kk; i++) {
dat1[i]=dgen[kk-1-i];
}
// Compute the parity symbols
encode_rs_sf(rs,dat1,b);
// Move parity symbols and data into sent[] array, in reverse order.
for (i = 0; i < nroots; i++) sent[nroots-1-i] = b[i];
for (i = 0; i < kk; i++) sent[i+nroots] = dat1[kk-1-i];
}
void rs_decode_(int *recd0, int *era0, int *numera0, int *decoded, int *nerr)
// Decode JT65 received data recd0[63], producing decoded[12].
// Erasures are indicated in era0[numera]. The number of corrected
// errors is *nerr. If the data are uncorrectable, *nerr=-1 is
// returned.
{
int numera;
int i;
int era_pos[200];
int recd[255];
numera=*numera0;
for(i=0; i<kk; i++) recd[i]=recd0[nn-1-i];
for(i=0; i<nroots; i++) recd[kk+i]=recd0[nroots-1-i];
if(numera)
for(i=0; i<numera; i++) era_pos[i]=era0[i];
*nerr=decode_rs_sf(rs,recd,era_pos,numera);
for(i=0; i<kk; i++) decoded[i]=recd[kk-1-i];
}

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lib/superfox/rs_sf.h Normal file
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/* User include file for the Reed-Solomon codec
* Copyright 2002, Phil Karn KA9Q
* May be used under the terms of the GNU General Public License (GPL)
*/
/* General purpose RS codec, 8-bit symbols */
void encode_rs_char(void *rs,unsigned char *data,unsigned char *parity);
int decode_rs_char(void *rs,unsigned char *data,int *eras_pos,
int no_eras);
void *init_rs_char(int symsize,int gfpoly,
int fcr,int prim,int nroots,
int pad);
void free_rs_char(void *rs);
/* General purpose RS codec, integer symbols */
void encode_rs_sf(void *rs,int *data,int *parity);
int decode_rs_sf(void *rs,int *data,int *eras_pos,int no_eras);
void *init_rs_sf(int symsize,int gfpoly,int fcr,
int prim,int nroots,int pad);
void free_rs_sf(void *rs);
/* CCSDS standard (255,223) RS codec with conventional (*not* dual-basis)
* symbol representation
*/
void encode_rs_8(unsigned char *data,unsigned char *parity,int pad);
int decode_rs_8(unsigned char *data,int *eras_pos,int no_eras,int pad);
/* CCSDS standard (255,223) RS codec with dual-basis symbol representation */
void encode_rs_ccsds(unsigned char *data,unsigned char *parity,int pad);
int decode_rs_ccsds(unsigned char *data,int *eras_pos,int no_eras,int pad);
/* Tables to map from conventional->dual (Taltab) and
* dual->conventional (Tal1tab) bases
*/
extern unsigned char Taltab[],Tal1tab[];