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Add support for FLEX pager protocol to multimon-ng
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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. | ||
*/ | ||
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#include <math.h> | ||
#include <stdlib.h> | ||
#include "BCHCode.h" | ||
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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) | ||
}; | ||
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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) | ||
*/ | ||
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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; | ||
} | ||
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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? :) | ||
*/ | ||
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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"); | ||
} | ||
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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) | ||
*/ | ||
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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; | ||
}; | ||
}; | ||
}; | ||
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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. | ||
*/ | ||
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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"); | ||
} | ||
} | ||
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return retval; | ||
} | ||
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/* | ||
* 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; | ||
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BCHCode_data=(struct BCHCode *) malloc(sizeof (struct BCHCode)); | ||
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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)); | ||
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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; | ||
} | ||
} | ||
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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; | ||
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generate_gf(BCHCode_data); /* generate the Galois Field GF(2**m) */ | ||
gen_poly(BCHCode_data); /* Compute the generator polynomial of BCH code */ | ||
} | ||
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return BCHCode_data; | ||
} | ||
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void BCHCode_Delete(struct BCHCode * BCHCode_data) { | ||
if (BCHCode_data==NULL) return; | ||
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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); | ||
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free(BCHCode_data); | ||
} |
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struct BCHCode; | ||
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struct BCHCode * BCHCode_New(int p[], int m, int n, int k, int t); | ||
void BCHCode_Delete(struct BCHCode * BCHCode_data); | ||
void BCHCode_Encode(struct BCHCode * BCHCode_data, int data[]); | ||
int BCHCode_Decode(struct BCHCode * BCHCode_data, int recd[]); |
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