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BCHCode.c
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BCHCode.c
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/*
* BCHCode.c
*
* Copyright (C) 2015 Craig Shelley (craig@microtron.org.uk)
*
* BCH Encoder/Decoder - Adapted from GNURadio for use with Multimon
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
#include <math.h>
#include <stdlib.h>
#include "BCHCode.h"
struct BCHCode {
int * p; // coefficients of primitive polynomial used to generate GF(2**5)
int m; // order of the field GF(2**5) = 5
int n; // 2**5 - 1 = 31
int k; // n - deg(g(x)) = 21 = dimension
int t; // 2 = error correcting capability
int * alpha_to; // log table of GF(2**5)
int * index_of; // antilog table of GF(2**5)
int * g; // coefficients of generator polynomial, g(x) [n - k + 1]=[11]
int * bb; // coefficients of redundancy polynomial ( x**(10) i(x) ) modulo g(x)
};
static void generate_gf(struct BCHCode * BCHCode_data) {
if (BCHCode_data==NULL) return;
/*
* generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m]
* lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
* polynomial form -> index form index_of[j=alpha**i] = i alpha=2 is the
* primitive element of GF(2**m)
*/
register int i, mask;
mask = 1;
BCHCode_data->alpha_to[BCHCode_data->m] = 0;
for (i = 0; i < BCHCode_data->m; i++) {
BCHCode_data->alpha_to[i] = mask;
BCHCode_data->index_of[BCHCode_data->alpha_to[i]] = i;
if (BCHCode_data->p[i] != 0)
BCHCode_data->alpha_to[BCHCode_data->m] ^= mask;
mask <<= 1;
}
BCHCode_data->index_of[BCHCode_data->alpha_to[BCHCode_data->m]] = BCHCode_data->m;
mask >>= 1;
for (i = BCHCode_data->m + 1; i < BCHCode_data->n; i++) {
if (BCHCode_data->alpha_to[i - 1] >= mask)
BCHCode_data->alpha_to[i] = BCHCode_data->alpha_to[BCHCode_data->m] ^ ((BCHCode_data->alpha_to[i - 1] ^ mask) << 1);
else
BCHCode_data->alpha_to[i] = BCHCode_data->alpha_to[i - 1] << 1;
BCHCode_data->index_of[BCHCode_data->alpha_to[i]] = i;
}
BCHCode_data->index_of[0] = -1;
}
static void gen_poly(struct BCHCode * BCHCode_data) {
if (BCHCode_data==NULL) return;
/*
* Compute generator polynomial of BCH code of length = 31, redundancy = 10
* (OK, this is not very efficient, but we only do it once, right? :)
*/
register int ii, jj, ll, kaux;
int test, aux, nocycles, root, noterms, rdncy;
int cycle[15][6], size[15], min[11], zeros[11];
/* Generate cycle sets modulo 31 */
cycle[0][0] = 0; size[0] = 1;
cycle[1][0] = 1; size[1] = 1;
jj = 1; /* cycle set index */
do {
/* Generate the jj-th cycle set */
ii = 0;
do {
ii++;
cycle[jj][ii] = (cycle[jj][ii - 1] * 2) % BCHCode_data->n;
size[jj]++;
aux = (cycle[jj][ii] * 2) % BCHCode_data->n;
} while (aux != cycle[jj][0]);
/* Next cycle set representative */
ll = 0;
do {
ll++;
test = 0;
for (ii = 1; ((ii <= jj) && (!test)); ii++) {
/* Examine previous cycle sets */
for (kaux = 0; ((kaux < size[ii]) && (!test)); kaux++) {
if (ll == cycle[ii][kaux]) {
test = 1;
}
}
}
} while ((test) && (ll < (BCHCode_data->n - 1)));
if (!(test)) {
jj++; /* next cycle set index */
cycle[jj][0] = ll;
size[jj] = 1;
}
} while (ll < (BCHCode_data->n - 1));
nocycles = jj; /* number of cycle sets modulo BCHCode_data->n */
/* Search for roots 1, 2, ..., BCHCode_data->d-1 in cycle sets */
kaux = 0;
rdncy = 0;
for (ii = 1; ii <= nocycles; ii++) {
min[kaux] = 0;
for (jj = 0; jj < size[ii]; jj++) {
for (root = 1; root < (2*BCHCode_data->t + 1); root++) {
if (root == cycle[ii][jj]) {
min[kaux] = ii;
}
}
}
if (min[kaux]) {
rdncy += size[min[kaux]];
kaux++;
}
}
noterms = kaux;
kaux = 1;
for (ii = 0; ii < noterms; ii++) {
for (jj = 0; jj < size[min[ii]]; jj++) {
zeros[kaux] = cycle[min[ii]][jj];
kaux++;
}
}
//printf("This is a (%d, %d, %d) binary BCH code\n", BCHCode_data->n, BCHCode_data->k, BCHCode_data->d);
/* Compute generator polynomial */
BCHCode_data->g[0] = BCHCode_data->alpha_to[zeros[1]];
BCHCode_data->g[1] = 1; /* g(x) = (X + zeros[1]) initially */
for (ii = 2; ii <= rdncy; ii++) {
BCHCode_data->g[ii] = 1;
for (jj = ii - 1; jj > 0; jj--) {
if (BCHCode_data->g[jj] != 0)
BCHCode_data->g[jj] = BCHCode_data->g[jj - 1] ^ BCHCode_data->alpha_to[(BCHCode_data->index_of[BCHCode_data->g[jj]] + zeros[ii]) % BCHCode_data->n];
else
BCHCode_data->g[jj] = BCHCode_data->g[jj - 1];
}
BCHCode_data->g[0] = BCHCode_data->alpha_to[(BCHCode_data->index_of[BCHCode_data->g[0]] + zeros[ii]) % BCHCode_data->n];
}
//printf("g(x) = ");
//for (ii = 0; ii <= rdncy; ii++) {
// printf("%d", BCHCode_data->g[ii]);
// if (ii && ((ii % 70) == 0)) {
// printf("\n");
// }
//}
//printf("\n");
}
void BCHCode_Encode(struct BCHCode * BCHCode_data, int data[]) {
if (BCHCode_data==NULL) return;
/*
* Calculate redundant bits bb[], codeword is c(X) = data(X)*X**(n-k)+ bb(X)
*/
register int i, j;
register int feedback;
for (i = 0; i < BCHCode_data->n - BCHCode_data->k; i++) {
BCHCode_data->bb[i] = 0;
}
for (i = BCHCode_data->k - 1; i >= 0; i--) {
feedback = data[i] ^ BCHCode_data->bb[BCHCode_data->n - BCHCode_data->k - 1];
if (feedback != 0) {
for (j = BCHCode_data->n - BCHCode_data->k - 1; j > 0; j--) {
if (BCHCode_data->g[j] != 0) {
BCHCode_data->bb[j] = BCHCode_data->bb[j - 1] ^ feedback;
} else {
BCHCode_data->bb[j] = BCHCode_data->bb[j - 1];
}
}
BCHCode_data->bb[0] = BCHCode_data->g[0] && feedback;
} else {
for (j = BCHCode_data->n - BCHCode_data->k - 1; j > 0; j--) {
BCHCode_data->bb[j] = BCHCode_data->bb[j - 1];
}
BCHCode_data->bb[0] = 0;
};
};
};
int BCHCode_Decode(struct BCHCode * BCHCode_data, int recd[]) {
if (BCHCode_data==NULL) return -1;
/*
* We do not need the Berlekamp algorithm to decode.
* We solve before hand two equations in two variables.
*/
register int i, j, q;
int elp[3], s[5], s3;
int count = 0, syn_error = 0;
int loc[3], reg[3];
int aux;
int retval=0;
/* first form the syndromes */
// printf("s[] = (");
for (i = 1; i <= 4; i++) {
s[i] = 0;
for (j = 0; j < BCHCode_data->n; j++) {
if (recd[j] != 0) {
s[i] ^= BCHCode_data->alpha_to[(i * j) % BCHCode_data->n];
}
}
if (s[i] != 0) {
syn_error = 1; /* set flag if non-zero syndrome */
}
/* NOTE: If only error detection is needed,
* then exit the program here...
*/
/* convert syndrome from polynomial form to index form */
s[i] = BCHCode_data->index_of[s[i]];
//printf("%3d ", s[i]);
};
//printf(")\n");
if (syn_error) { /* If there are errors, try to correct them */
if (s[1] != -1) {
s3 = (s[1] * 3) % BCHCode_data->n;
if ( s[3] == s3 ) { /* Was it a single error ? */
//printf("One error at %d\n", s[1]);
recd[s[1]] ^= 1; /* Yes: Correct it */
} else {
/* Assume two errors occurred and solve
* for the coefficients of sigma(x), the
* error locator polynomail
*/
if (s[3] != -1) {
aux = BCHCode_data->alpha_to[s3] ^ BCHCode_data->alpha_to[s[3]];
} else {
aux = BCHCode_data->alpha_to[s3];
}
elp[0] = 0;
elp[1] = (s[2] - BCHCode_data->index_of[aux] + BCHCode_data->n) % BCHCode_data->n;
elp[2] = (s[1] - BCHCode_data->index_of[aux] + BCHCode_data->n) % BCHCode_data->n;
//printf("sigma(x) = ");
//for (i = 0; i <= 2; i++) {
// printf("%3d ", elp[i]);
//}
//printf("\n");
//printf("Roots: ");
/* find roots of the error location polynomial */
for (i = 1; i <= 2; i++) {
reg[i] = elp[i];
}
count = 0;
for (i = 1; i <= BCHCode_data->n; i++) { /* Chien search */
q = 1;
for (j = 1; j <= 2; j++) {
if (reg[j] != -1) {
reg[j] = (reg[j] + j) % BCHCode_data->n;
q ^= BCHCode_data->alpha_to[reg[j]];
}
}
if (!q) { /* store error location number indices */
loc[count] = i % BCHCode_data->n;
count++;
//printf("%3d ", (i%n));
}
}
//printf("\n");
if (count == 2) {
/* no. roots = degree of elp hence 2 errors */
for (i = 0; i < 2; i++)
recd[loc[i]] ^= 1;
} else { /* Cannot solve: Error detection */
retval=1;
//for (i = 0; i < 31; i++) {
// recd[i] = 0;
//}
//printf("incomplete decoding\n");
}
}
} else if (s[2] != -1) {/* Error detection */
retval=1;
//for (i = 0; i < 31; i++) recd[i] = 0;
//printf("incomplete decoding\n");
}
}
return retval;
}
/*
* Example usage BCH(31,21,5)
*
* p[] = coefficients of primitive polynomial used to generate GF(2**5)
* m = order of the field GF(2**5) = 5
* n = 2**5 - 1 = 31
* t = 2 = error correcting capability
* d = 2*BCHCode_data->t + 1 = 5 = designed minimum distance
* k = n - deg(g(x)) = 21 = dimension
* g[] = coefficients of generator polynomial, g(x) [n - k + 1]=[11]
* alpha_to [] = log table of GF(2**5)
* index_of[] = antilog table of GF(2**5)
* data[] = coefficients of data polynomial, i(x)
* bb[] = coefficients of redundancy polynomial ( x**(10) i(x) ) modulo g(x)
*/
struct BCHCode * BCHCode_New(int p[], int m, int n, int k, int t) {
struct BCHCode * BCHCode_data=NULL;
BCHCode_data=(struct BCHCode *) malloc(sizeof (struct BCHCode));
if (BCHCode_data!=NULL) {
BCHCode_data->alpha_to=(int *) malloc(sizeof(int) * (n+1));
BCHCode_data->index_of=(int *) malloc(sizeof(int) * (n+1));
BCHCode_data->p=(int *) malloc(sizeof(int) * (m+1));
BCHCode_data->g=(int *) malloc(sizeof(int) * (n-k+1));
BCHCode_data->bb=(int *) malloc(sizeof(int) * (n-k+1));
if (
BCHCode_data->alpha_to == NULL ||
BCHCode_data->index_of == NULL ||
BCHCode_data->p == NULL ||
BCHCode_data->g == NULL ||
BCHCode_data->bb == NULL
) {
BCHCode_Delete(BCHCode_data);
BCHCode_data=NULL;
}
}
if (BCHCode_data!=NULL) {
int i;
for (i=0; i<(m+1); i++) {
BCHCode_data->p[i]=p[i];
}
BCHCode_data->m=m;
BCHCode_data->n=n;
BCHCode_data->k=k;
BCHCode_data->t=t;
generate_gf(BCHCode_data); /* generate the Galois Field GF(2**m) */
gen_poly(BCHCode_data); /* Compute the generator polynomial of BCH code */
}
return BCHCode_data;
}
void BCHCode_Delete(struct BCHCode * BCHCode_data) {
if (BCHCode_data==NULL) return;
if (BCHCode_data->alpha_to != NULL) free(BCHCode_data->alpha_to);
if (BCHCode_data->index_of != NULL) free(BCHCode_data->index_of);
if (BCHCode_data->p != NULL) free(BCHCode_data->p);
if (BCHCode_data->g != NULL) free(BCHCode_data->g);
if (BCHCode_data->bb != NULL) free(BCHCode_data->bb);
free(BCHCode_data);
}