HackRF-Treasure-Chest/Software/portapack-mayhem/firmware/common/bch_code.cpp

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2022-09-22 18:26:57 +02:00
/*
* Copyright (C) 2015 Craig Shelley (craig@microtron.org.uk)
* Copyright (C) 2016 Furrtek
*
* BCH Encoder/Decoder - Adapted from GNURadio
*
* This file is part of PortaPack.
*
* 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, 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; see the file COPYING. If not, write to
* the Free Software Foundation, Inc., 51 Franklin Street,
* Boston, MA 02110-1301, USA.
*/
#include <math.h>
#include <stdlib.h>
#include <ch.h>
#include "bch_code.hpp"
void BCHCode::generate_gf() {
/*
* 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)
*/
int i, mask;
mask = 1;
alpha_to[m] = 0;
for (i = 0; i < m; i++)
{
alpha_to[i] = mask;
index_of[alpha_to[i]] = i;
if (p[i] != 0)
alpha_to[m] ^= mask;
mask <<= 1;
}
index_of[alpha_to[m]] = m;
mask >>= 1;
for (i = m + 1; i < n; i++)
{
if (alpha_to[i - 1] >= mask)
alpha_to[i] = alpha_to[m] ^ ((alpha_to[i - 1] ^ mask) << 1);
else
alpha_to[i] = alpha_to[i - 1] << 1;
index_of[alpha_to[i]] = i;
}
index_of[0] = -1;
}
void BCHCode::gen_poly() {
/*
* Compute generator polynomial of BCH code of length = 31, redundancy = 10
* (OK, this is not very efficient, but we only do it once, right? :)
*/
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) % n;
size[jj]++;
aux = (cycle[jj][ii] * 2) % 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 < (n - 1)));
if (!(test))
{
jj++; // next cycle set index
cycle[jj][0] = ll;
size[jj] = 1;
}
} while (ll < (n - 1));
nocycles = jj; // number of cycle sets modulo n
// Search for roots 1, 2, ..., 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 < d; 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++;
}
// Compute generator polynomial
g[0] = alpha_to[zeros[1]];
g[1] = 1; // g(x) = (X + zeros[1]) initially
for (ii = 2; ii <= rdncy; ii++)
{
g[ii] = 1;
for (jj = ii - 1; jj > 0; jj--)
if (g[jj] != 0)
g[jj] = g[jj - 1] ^ alpha_to[(index_of[g[jj]] + zeros[ii]) % n];
else
g[jj] = g[jj - 1];
g[0] = alpha_to[(index_of[g[0]] + zeros[ii]) % n];
}
}
int * BCHCode::encode(int data[]) {
// Calculate redundant bits bb[]
int h, i, j=0, start=0, end=(n-k); // 10
int Mr[31];
if (!valid) return nullptr;
for (i = 0; i < n; i++) {
Mr[i] = 0;
}
for (h = 0; h < k; ++h)
Mr[h] = data[h];
while (end < n)
{
for (i=end; i>start-2; --i)
{
if (Mr[start] != 0)
{
Mr[i]^=g[j];
++j;
}
else
{
++start;
j = 0;
end = start+(n-k);
break;
}
}
}
j = 0;
for (i = start; i<end; ++i) {
bb[j]=Mr[i];
++j;
}
return bb;
};
int BCHCode::decode(int recd[]) {
// We do not need the Berlekamp algorithm to decode.
// We solve before hand two equations in two variables.
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;
if (!valid) return 0;
for (i = 1; i <= 4; i++) {
s[i] = 0;
for (j = 0; j < n; j++) {
if (recd[j] != 0) {
s[i] ^= alpha_to[(i * j) % 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] = index_of[s[i]];
};
if (syn_error) { // If there are errors, try to correct them
if (s[1] != -1) {
s3 = (s[1] * 3) % 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 polynomial
*/
if (s[3] != -1) {
aux = alpha_to[s3] ^ alpha_to[s[3]];
} else {
aux = alpha_to[s3];
}
elp[0] = 0;
elp[1] = (s[2] - index_of[aux] + n) % n;
elp[2] = (s[1] - index_of[aux] + n) % 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 <= n; i++) { // Chien search
q = 1;
for (j = 1; j <= 2; j++) {
if (reg[j] != -1) {
reg[j] = (reg[j] + j) % n;
q ^= alpha_to[reg[j]];
}
}
if (!q) { // store error location number indices
loc[count] = i % n;
count++;
}
}
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;
}
}
} else if (s[2] != -1) { // Error detection
retval=1;
}
}
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*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)
*/
BCHCode::BCHCode(
std::vector<int> p_init, int m, int n, int k, int t
) : m { m },
n { n },
k { k },
t { t } {
size_t i;
d = 5;
alpha_to = (int *)chHeapAlloc(NULL, sizeof(int) * (n + 1));
index_of = (int *)chHeapAlloc(0, sizeof(int) * (n + 1));
p = (int *)chHeapAlloc(0, sizeof(int) * (m + 1));
g = (int *)chHeapAlloc(0, sizeof(int) * (n - k + 1));
bb = (int *)chHeapAlloc(0, sizeof(int) * (n - k + 1));
if (alpha_to == NULL ||
index_of == NULL ||
p == NULL ||
g == NULL ||
bb == NULL)
valid = false;
else
valid = true;
if (valid) {
for (i = 0; i < (size_t)(m + 1); i++) {
p[i] = p_init[i];
}
generate_gf(); /* generate the Galois Field GF(2**m) */
gen_poly(); /* Compute the generator polynomial of BCH code */
}
}
BCHCode::~BCHCode() {
if (alpha_to != NULL) chHeapFree(alpha_to);
if (index_of != NULL) chHeapFree(index_of);
if (p != NULL) chHeapFree(p);
if (g != NULL) chHeapFree(g);
if (bb != NULL) chHeapFree(bb);
}