365 lines
7.8 KiB
C++
365 lines
7.8 KiB
C++
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/*
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* Copyright (C) 2015 Craig Shelley (craig@microtron.org.uk)
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* Copyright (C) 2016 Furrtek
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*
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* BCH Encoder/Decoder - Adapted from GNURadio
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*
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* This file is part of PortaPack.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 2, or (at your option)
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* any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; see the file COPYING. If not, write to
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* the Free Software Foundation, Inc., 51 Franklin Street,
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* Boston, MA 02110-1301, USA.
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*/
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#include <math.h>
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#include <stdlib.h>
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#include <ch.h>
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#include "bch_code.hpp"
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void BCHCode::generate_gf() {
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/*
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* generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m]
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* lookup tables: index->polynomial form alpha_to[] contains j=alpha**i;
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* polynomial form -> index form index_of[j=alpha**i] = i alpha=2 is the
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* primitive element of GF(2**m)
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*/
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int i, mask;
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mask = 1;
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alpha_to[m] = 0;
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for (i = 0; i < m; i++)
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{
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alpha_to[i] = mask;
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index_of[alpha_to[i]] = i;
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if (p[i] != 0)
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alpha_to[m] ^= mask;
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mask <<= 1;
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}
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index_of[alpha_to[m]] = m;
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mask >>= 1;
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for (i = m + 1; i < n; i++)
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{
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if (alpha_to[i - 1] >= mask)
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alpha_to[i] = alpha_to[m] ^ ((alpha_to[i - 1] ^ mask) << 1);
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else
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alpha_to[i] = alpha_to[i - 1] << 1;
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index_of[alpha_to[i]] = i;
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}
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index_of[0] = -1;
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}
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void BCHCode::gen_poly() {
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/*
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* Compute generator polynomial of BCH code of length = 31, redundancy = 10
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* (OK, this is not very efficient, but we only do it once, right? :)
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*/
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int ii, jj, ll, kaux;
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int test, aux, nocycles, root, noterms, rdncy;
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int cycle[15][6], size[15], min[11], zeros[11];
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// Generate cycle sets modulo 31
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cycle[0][0] = 0; size[0] = 1;
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cycle[1][0] = 1; size[1] = 1;
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jj = 1; // cycle set index
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do
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{
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// Generate the jj-th cycle set
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ii = 0;
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do
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{
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ii++;
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cycle[jj][ii] = (cycle[jj][ii - 1] * 2) % n;
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size[jj]++;
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aux = (cycle[jj][ii] * 2) % n;
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} while (aux != cycle[jj][0]);
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// Next cycle set representative
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ll = 0;
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do
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{
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ll++;
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test = 0;
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for (ii = 1; ((ii <= jj) && (!test)); ii++)
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// Examine previous cycle sets
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for (kaux = 0; ((kaux < size[ii]) && (!test)); kaux++)
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if (ll == cycle[ii][kaux])
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test = 1;
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}
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while ((test) && (ll < (n - 1)));
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if (!(test))
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{
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jj++; // next cycle set index
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cycle[jj][0] = ll;
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size[jj] = 1;
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}
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} while (ll < (n - 1));
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nocycles = jj; // number of cycle sets modulo n
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// Search for roots 1, 2, ..., d-1 in cycle sets
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kaux = 0;
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rdncy = 0;
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for (ii = 1; ii <= nocycles; ii++)
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{
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min[kaux] = 0;
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for (jj = 0; jj < size[ii]; jj++)
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for (root = 1; root < d; root++)
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if (root == cycle[ii][jj])
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min[kaux] = ii;
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if (min[kaux])
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{
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rdncy += size[min[kaux]];
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kaux++;
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}
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}
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noterms = kaux;
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kaux = 1;
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for (ii = 0; ii < noterms; ii++)
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for (jj = 0; jj < size[min[ii]]; jj++)
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{
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zeros[kaux] = cycle[min[ii]][jj];
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kaux++;
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}
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// Compute generator polynomial
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g[0] = alpha_to[zeros[1]];
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g[1] = 1; // g(x) = (X + zeros[1]) initially
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for (ii = 2; ii <= rdncy; ii++)
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{
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g[ii] = 1;
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for (jj = ii - 1; jj > 0; jj--)
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if (g[jj] != 0)
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g[jj] = g[jj - 1] ^ alpha_to[(index_of[g[jj]] + zeros[ii]) % n];
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else
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g[jj] = g[jj - 1];
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g[0] = alpha_to[(index_of[g[0]] + zeros[ii]) % n];
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}
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}
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int * BCHCode::encode(int data[]) {
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// Calculate redundant bits bb[]
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int h, i, j=0, start=0, end=(n-k); // 10
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int Mr[31];
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if (!valid) return nullptr;
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for (i = 0; i < n; i++) {
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Mr[i] = 0;
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}
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for (h = 0; h < k; ++h)
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Mr[h] = data[h];
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while (end < n)
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{
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for (i=end; i>start-2; --i)
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{
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if (Mr[start] != 0)
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{
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Mr[i]^=g[j];
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++j;
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}
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else
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{
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++start;
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j = 0;
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end = start+(n-k);
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break;
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}
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}
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}
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j = 0;
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for (i = start; i<end; ++i) {
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bb[j]=Mr[i];
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++j;
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}
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return bb;
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};
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int BCHCode::decode(int recd[]) {
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// We do not need the Berlekamp algorithm to decode.
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// We solve before hand two equations in two variables.
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int i, j, q;
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int elp[3], s[5], s3;
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int count = 0, syn_error = 0;
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int loc[3], reg[3];
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int aux;
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int retval=0;
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if (!valid) return 0;
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for (i = 1; i <= 4; i++) {
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s[i] = 0;
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for (j = 0; j < n; j++) {
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if (recd[j] != 0) {
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s[i] ^= alpha_to[(i * j) % n];
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}
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}
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if (s[i] != 0) {
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syn_error = 1; // set flag if non-zero syndrome
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}
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/* NOTE: If only error detection is needed,
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* then exit the program here...
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*/
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// Convert syndrome from polynomial form to index form
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s[i] = index_of[s[i]];
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};
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if (syn_error) { // If there are errors, try to correct them
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if (s[1] != -1) {
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s3 = (s[1] * 3) % n;
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if ( s[3] == s3 ) { // Was it a single error ?
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//printf("One error at %d\n", s[1]);
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recd[s[1]] ^= 1; // Yes: Correct it
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} else {
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/* Assume two errors occurred and solve
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* for the coefficients of sigma(x), the
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* error locator polynomial
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*/
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if (s[3] != -1) {
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aux = alpha_to[s3] ^ alpha_to[s[3]];
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} else {
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aux = alpha_to[s3];
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}
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elp[0] = 0;
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elp[1] = (s[2] - index_of[aux] + n) % n;
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elp[2] = (s[1] - index_of[aux] + n) % n;
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//printf("sigma(x) = ");
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//for (i = 0; i <= 2; i++) {
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// printf("%3d ", elp[i]);
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//}
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//printf("\n");
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//printf("Roots: ");
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// Find roots of the error location polynomial
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for (i = 1; i <= 2; i++) {
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reg[i] = elp[i];
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}
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count = 0;
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for (i = 1; i <= n; i++) { // Chien search
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q = 1;
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for (j = 1; j <= 2; j++) {
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if (reg[j] != -1) {
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reg[j] = (reg[j] + j) % n;
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q ^= alpha_to[reg[j]];
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}
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}
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if (!q) { // store error location number indices
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loc[count] = i % n;
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count++;
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}
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}
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if (count == 2) {
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// no. roots = degree of elp hence 2 errors
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for (i = 0; i < 2; i++)
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recd[loc[i]] ^= 1;
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} else { // Cannot solve: Error detection
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retval=1;
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}
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}
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} else if (s[2] != -1) { // Error detection
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retval=1;
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}
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}
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return retval;
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}
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/*
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* Example usage BCH(31,21,5)
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*
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* p[] = coefficients of primitive polynomial used to generate GF(2**5)
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* m = order of the field GF(2**5) = 5
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* n = 2**5 - 1 = 31
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* t = 2 = error correcting capability
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* d = 2*t + 1 = 5 = designed minimum distance
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* k = n - deg(g(x)) = 21 = dimension
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* g[] = coefficients of generator polynomial, g(x) [n - k + 1]=[11]
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* alpha_to [] = log table of GF(2**5)
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* index_of[] = antilog table of GF(2**5)
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* data[] = coefficients of data polynomial, i(x)
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* bb[] = coefficients of redundancy polynomial ( x**(10) i(x) ) modulo g(x)
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*/
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BCHCode::BCHCode(
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std::vector<int> p_init, int m, int n, int k, int t
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) : m { m },
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n { n },
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k { k },
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t { t } {
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size_t i;
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d = 5;
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alpha_to = (int *)chHeapAlloc(NULL, sizeof(int) * (n + 1));
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index_of = (int *)chHeapAlloc(0, sizeof(int) * (n + 1));
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p = (int *)chHeapAlloc(0, sizeof(int) * (m + 1));
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g = (int *)chHeapAlloc(0, sizeof(int) * (n - k + 1));
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bb = (int *)chHeapAlloc(0, sizeof(int) * (n - k + 1));
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if (alpha_to == NULL ||
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index_of == NULL ||
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p == NULL ||
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g == NULL ||
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bb == NULL)
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valid = false;
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else
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valid = true;
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if (valid) {
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for (i = 0; i < (size_t)(m + 1); i++) {
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p[i] = p_init[i];
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}
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generate_gf(); /* generate the Galois Field GF(2**m) */
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gen_poly(); /* Compute the generator polynomial of BCH code */
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}
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}
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BCHCode::~BCHCode() {
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if (alpha_to != NULL) chHeapFree(alpha_to);
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if (index_of != NULL) chHeapFree(index_of);
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if (p != NULL) chHeapFree(p);
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if (g != NULL) chHeapFree(g);
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if (bb != NULL) chHeapFree(bb);
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}
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