mirror of https://github.com/wb2osz/direwolf.git
Added derived code to calc/apply BCH codes.
This commit is contained in:
David E. Tiller
parent
26ac27bf57
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d898d1b4c4
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/*
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* File: bch3.c
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* Title: Encoder/decoder for binary BCH codes in C (Version 3.1)
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* Author: Robert Morelos-Zaragoza
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* Date: August 1994
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* Revised: June 13, 1997
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*
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* =============== Encoder/Decoder for binary BCH codes in C =================
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*
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* Version 1: Original program. The user provides the generator polynomial
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* of the code (cumbersome!).
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* Version 2: Computes the generator polynomial of the code.
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* Version 3: No need to input the coefficients of a primitive polynomial of
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* degree m, used to construct the Galois Field GF(2**m). The
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* program now works for any binary BCH code of length such that:
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* 2**(m-1) - 1 < length <= 2**m - 1
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*
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* Note: You may have to change the size of the arrays to make it work.
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*
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* The encoding and decoding methods used in this program are based on the
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* book "Error Control Coding: Fundamentals and Applications", by Lin and
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* Costello, Prentice Hall, 1983.
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*
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* Thanks to Patrick Boyle (pboyle@era.com) for his observation that 'bch2.c'
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* did not work for lengths other than 2**m-1 which led to this new version.
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* Portions of this program are from 'rs.c', a Reed-Solomon encoder/decoder
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* in C, written by Simon Rockliff (simon@augean.ua.oz.au) on 21/9/89. The
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* previous version of the BCH encoder/decoder in C, 'bch2.c', was written by
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* Robert Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) on 5/19/92.
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*
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* NOTE:
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* The author is not responsible for any malfunctioning of
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* this program, nor for any damage caused by it. Please include the
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* original program along with these comments in any redistribution.
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*
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* For more information, suggestions, or other ideas on implementing error
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* correcting codes, please contact me at:
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*
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* Robert Morelos-Zaragoza
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* 5120 Woodway, Suite 7036
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* Houston, Texas 77056
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*
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* email: r.morelos-zaragoza@ieee.org
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*
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* COPYRIGHT NOTICE: This computer program is free for non-commercial purposes.
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* You may implement this program for any non-commercial application. You may
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* also implement this program for commercial purposes, provided that you
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* obtain my written permission. Any modification of this program is covered
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* by this copyright.
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*
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* == Copyright (c) 1994-7, Robert Morelos-Zaragoza. All rights reserved. ==
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*
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* m = order of the Galois field GF(2**m)
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* n = 2**m - 1 = size of the multiplicative group of GF(2**m)
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* length = length of the BCH code
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* t = error correcting capability (max. no. of errors the code corrects)
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* d = 2*t + 1 = designed min. distance = no. of consecutive roots of g(x) + 1
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* k = n - deg(g(x)) = dimension (no. of information bits/codeword) of the code
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* p[] = coefficients of a primitive polynomial used to generate GF(2**m)
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* g[] = coefficients of the generator polynomial, g(x)
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* alpha_to [] = log table of GF(2**m)
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* index_of[] = antilog table of GF(2**m)
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* data[] = information bits = coefficients of data polynomial, i(x)
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* bb[] = coefficients of redundancy polynomial x^(length-k) i(x) modulo g(x)
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* numerr = number of errors
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* errpos[] = error positions
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* recd[] = coefficients of the received polynomial
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* decerror = number of decoding errors (in _message_ positions)
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*
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*/
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#include <math.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include "bch.h"
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int bch_init(bch_t *bch, int m, int length, int t) {
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int p[21], n;
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if (bch == NULL) {
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return -1;
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}
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if (m < 2 || m > 20) {
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return -2;
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}
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bch->m = m;
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bch->length = length;
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bch->t = t;
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for (int i=1; i<m; i++) {
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p[i] = 0;
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}
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p[0] = p[m] = 1;
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if (m == 2) p[1] = 1;
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else if (m == 3) p[1] = 1;
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else if (m == 4) p[1] = 1;
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else if (m == 5) p[2] = 1;
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else if (m == 6) p[1] = 1;
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else if (m == 7) p[1] = 1;
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else if (m == 8) p[4] = p[5] = p[6] = 1;
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else if (m == 9) p[4] = 1;
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else if (m == 10) p[3] = 1;
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else if (m == 11) p[2] = 1;
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else if (m == 12) p[3] = p[4] = p[7] = 1;
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else if (m == 13) p[1] = p[3] = p[4] = 1;
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else if (m == 14) p[1] = p[11] = p[12] = 1;
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else if (m == 15) p[1] = 1;
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else if (m == 16) p[2] = p[3] = p[5] = 1;
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else if (m == 17) p[3] = 1;
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else if (m == 18) p[7] = 1;
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else if (m == 19) p[1] = p[5] = p[6] = 1;
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else if (m == 20) p[3] = 1;
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printf("p(x) = ");
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n = 1;
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for (int i = 0; i <= m; i++) {
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n *= 2;
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printf("%1d", p[i]);
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}
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printf("\n");
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n = n / 2 - 1;
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bch->n = n;
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int ninf = (n + 1) / 2 - 1;
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if (length < ninf || length > n) {
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return -3;
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}
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/*
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* Generate field GF(2**m) from the irreducible polynomial p(X) with
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* coefficients in p[0]..p[m].
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*
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* Lookup tables:
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* index->polynomial form: alpha_to[] contains j=alpha^i;
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* polynomial form -> index form: index_of[j=alpha^i] = i
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*
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* alpha=2 is the primitive element of GF(2**m)
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*/
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register int i, mask;
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bch->alpha_to = malloc(n * sizeof(int));
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bch->index_of = malloc(n * sizeof(int));
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mask = 1;
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bch->alpha_to[m] = 0;
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for (int i = 0; i < m; i++) {
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bch->alpha_to[i] = mask;
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bch->index_of[bch->alpha_to[i]] = i;
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if (p[i] != 0)
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bch->alpha_to[m] ^= mask;
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mask <<= 1;
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}
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bch->index_of[bch->alpha_to[m]] = m;
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mask >>= 1;
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for (int i = m + 1; i < n; i++) {
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if (bch->alpha_to[i - 1] >= mask)
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bch->alpha_to[i] = bch->alpha_to[m] ^ ((bch->alpha_to[i - 1] ^ mask) << 1);
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else
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bch->alpha_to[i] = bch->alpha_to[i - 1] << 1;
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bch->index_of[bch->alpha_to[i]] = i;
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}
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bch->index_of[0] = -1;
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/*
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* Compute the generator polynomial of a binary BCH code. Fist generate the
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* cycle sets modulo 2**m - 1, cycle[][] = (i, 2*i, 4*i, ..., 2^l*i). Then
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* determine those cycle sets that contain integers in the set of (d-1)
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* consecutive integers {1..(d-1)}. The generator polynomial is calculated
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* as the product of linear factors of the form (x+alpha^i), for every i in
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* the above cycle sets.
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*/
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register int ii, jj, ll, kaux;
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register int test, aux, nocycles, root, noterms, rdncy;
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int cycle[1024][21], size[1024], min[1024], zeros[1024];
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/* Generate cycle sets modulo n, n = 2**m - 1 */
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cycle[0][0] = 0;
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size[0] = 1;
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cycle[1][0] = 1;
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size[1] = 1;
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jj = 1; /* cycle set index */
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if (bch->m > 9) {
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printf("Computing cycle sets modulo %d\n", bch->n);
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printf("(This may take some time)...\n");
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}
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do {
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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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ii++;
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cycle[jj][ii] = (cycle[jj][ii - 1] * 2) % bch->n;
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size[jj]++;
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aux = (cycle[jj][ii] * 2) % bch->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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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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} while ((test) && (ll < (bch->n - 1)));
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if (!(test)) {
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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 < (bch->n - 1));
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nocycles = jj; /* number of cycle sets modulo n */
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int d = 2 * t + 1;
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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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min[kaux] = 0;
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test = 0;
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for (jj = 0; ((jj < size[ii]) && (!test)); jj++)
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for (root = 1; ((root < d) && (!test)); root++)
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if (root == cycle[ii][jj]) {
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test = 1;
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min[kaux] = ii;
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}
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if (min[kaux]) {
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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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zeros[kaux] = cycle[min[ii]][jj];
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kaux++;
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}
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bch-> k = length - rdncy;
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if (bch->k<0)
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{
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printf("Parameters invalid!\n");
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return -4;
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}
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printf("This is a (%d, %d, %d) binary BCH code\n", bch->length, bch->k, d);
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/* Compute the generator polynomial */
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bch->g = malloc(rdncy * sizeof(int));
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bch->g[0] = bch->alpha_to[zeros[1]];
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bch->g[1] = 1; /* g(x) = (X + zeros[1]) initially */
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for (ii = 2; ii <= rdncy; ii++) {
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bch->g[ii] = 1;
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for (jj = ii - 1; jj > 0; jj--)
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if (bch->g[jj] != 0)
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bch->g[jj] = bch->g[jj - 1] ^ bch->alpha_to[(bch->index_of[bch->g[jj]] + zeros[ii]) % bch->n];
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else
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bch->g[jj] = bch->g[jj - 1];
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bch->g[0] = bch->alpha_to[(bch->index_of[bch->g[0]] + zeros[ii]) % bch->n];
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}
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printf("Generator polynomial:\ng(x) = ");
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for (ii = 0; ii <= rdncy; ii++) {
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printf("%d", bch->g[ii]);
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}
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printf("\n");
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return 0;
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}
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void generate_bch(bch_t *bch, int *data, int *bb) {
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/*
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* Compute redundacy bb[], the coefficients of b(x). The redundancy
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* polynomial b(x) is the remainder after dividing x^(length-k)*data(x)
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* by the generator polynomial g(x).
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*/
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register int feedback;
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for (int i = 0; i < bch->length - bch->k; i++)
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bb[i] = 0;
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for (int i = bch->k - 1; i >= 0; i--) {
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feedback = data[i] ^ bb[bch->length - bch->k - 1];
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if (feedback != 0) {
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for (int j = bch->length - bch->k - 1; j > 0; j--)
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if (bch->g[j] != 0)
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bb[j] = bb[j - 1] ^ feedback;
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else
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bb[j] = bb[j - 1];
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bb[0] = bch->g[0] && feedback;
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} else {
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for (int j = bch->length - bch->k - 1; j > 0; j--)
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bb[j] = bb[j - 1];
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bb[0] = 0;
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}
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}
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}
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int
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apply_bch(bch_t *bch, int *recd)
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/*
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* Simon Rockliff's implementation of Berlekamp's algorithm.
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*
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* Assume we have received bits in recd[i], i=0..(n-1).
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*
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* Compute the 2*t syndromes by substituting alpha^i into rec(X) and
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* evaluating, storing the syndromes in s[i], i=1..2t (leave s[0] zero) .
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* Then we use the Berlekamp algorithm to find the error location polynomial
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* elp[i].
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*
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* If the degree of the elp is >t, then we cannot correct all the errors, and
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* we have detected an uncorrectable error pattern. We output the information
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* bits uncorrected.
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*
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* If the degree of elp is <=t, we substitute alpha^i , i=1..n into the elp
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* to get the roots, hence the inverse roots, the error location numbers.
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* This step is usually called "Chien's search".
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*
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* If the number of errors located is not equal the degree of the elp, then
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* the decoder assumes that there are more than t errors and cannot correct
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* them, only detect them. We output the information bits uncorrected.
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*/
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{
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register int i, j, u, q, t2, count = 0, syn_error = 0;
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int elp[1026][1024], d[1026], l[1026], u_lu[1026], s[1025];
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int root[200], loc[200], err[1024], reg[201];
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t2 = 2 * bch->t;
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/* first form the syndromes */
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printf("S(x) = ");
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for (i = 1; i <= t2; i++) {
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s[i] = 0;
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for (j = 0; j < bch->length; j++)
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if (recd[j] != 0)
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s[i] ^= bch->alpha_to[(i * j) % bch->n];
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if (s[i] != 0)
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syn_error = 1; /* set error flag if non-zero syndrome */
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/*
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* Note: If the code is used only for ERROR DETECTION, then
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* exit program here indicating the presence of errors.
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*/
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/* convert syndrome from polynomial form to index form */
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s[i] = bch->index_of[s[i]];
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printf("%3d ", s[i]);
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}
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printf("\n");
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if (syn_error) { /* if there are errors, try to correct them */
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/*
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* Compute the error location polynomial via the Berlekamp
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* iterative algorithm. Following the terminology of Lin and
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* Costello's book : d[u] is the 'mu'th discrepancy, where
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* u='mu'+1 and 'mu' (the Greek letter!) is the step number
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* ranging from -1 to 2*t (see L&C), l[u] is the degree of
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* the elp at that step, and u_l[u] is the difference between
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* the step number and the degree of the elp.
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*/
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/* initialise table entries */
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d[0] = 0; /* index form */
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d[1] = s[1]; /* index form */
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elp[0][0] = 0; /* index form */
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elp[1][0] = 1; /* polynomial form */
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for (i = 1; i < t2; i++) {
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elp[0][i] = -1; /* index form */
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elp[1][i] = 0; /* polynomial form */
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}
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l[0] = 0;
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l[1] = 0;
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u_lu[0] = -1;
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u_lu[1] = 0;
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u = 0;
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do {
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u++;
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if (d[u] == -1) {
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l[u + 1] = l[u];
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for (i = 0; i <= l[u]; i++) {
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elp[u + 1][i] = elp[u][i];
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elp[u][i] = bch->index_of[elp[u][i]];
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}
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} else
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/*
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* search for words with greatest u_lu[q] for
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* which d[q]!=0
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*/
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{
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q = u - 1;
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while ((d[q] == -1) && (q > 0))
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q--;
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/* have found first non-zero d[q] */
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if (q > 0) {
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j = q;
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do {
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j--;
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if ((d[j] != -1) && (u_lu[q] < u_lu[j]))
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q = j;
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} while (j > 0);
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}
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/*
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* have now found q such that d[u]!=0 and
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* u_lu[q] is maximum
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*/
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/* store degree of new elp polynomial */
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if (l[u] > l[q] + u - q)
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l[u + 1] = l[u];
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else
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l[u + 1] = l[q] + u - q;
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/* form new elp(x) */
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for (i = 0; i < t2; i++)
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elp[u + 1][i] = 0;
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for (i = 0; i <= l[q]; i++)
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if (elp[q][i] != -1)
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elp[u + 1][i + u - q] =
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bch->alpha_to[(d[u] + bch->n - d[q] + elp[q][i]) % bch->n];
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for (i = 0; i <= l[u]; i++) {
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elp[u + 1][i] ^= elp[u][i];
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elp[u][i] = bch->index_of[elp[u][i]];
|
||||
}
|
||||
}
|
||||
u_lu[u + 1] = u - l[u + 1];
|
||||
|
||||
/* form (u+1)th discrepancy */
|
||||
if (u < t2) {
|
||||
/* no discrepancy computed on last iteration */
|
||||
if (s[u + 1] != -1)
|
||||
d[u + 1] = bch->alpha_to[s[u + 1]];
|
||||
else
|
||||
d[u + 1] = 0;
|
||||
for (i = 1; i <= l[u + 1]; i++)
|
||||
if ((s[u + 1 - i] != -1) && (elp[u + 1][i] != 0))
|
||||
d[u + 1] ^= bch->alpha_to[(s[u + 1 - i]
|
||||
+ bch->index_of[elp[u + 1][i]]) % bch->n];
|
||||
/* put d[u+1] into index form */
|
||||
d[u + 1] = bch->index_of[d[u + 1]];
|
||||
}
|
||||
} while ((u < t2) && (l[u + 1] <= bch->t));
|
||||
|
||||
u++;
|
||||
if (l[u] <= bch->t) {/* Can correct errors */
|
||||
/* put elp into index form */
|
||||
for (i = 0; i <= l[u]; i++)
|
||||
elp[u][i] = bch->index_of[elp[u][i]];
|
||||
|
||||
printf("sigma(x) = ");
|
||||
for (i = 0; i <= l[u]; i++)
|
||||
printf("%3d ", elp[u][i]);
|
||||
printf("\n");
|
||||
printf("Roots: ");
|
||||
|
||||
/* Chien search: find roots of the error location polynomial */
|
||||
for (i = 1; i <= l[u]; i++)
|
||||
reg[i] = elp[u][i];
|
||||
count = 0;
|
||||
for (i = 1; i <= bch->n; i++) {
|
||||
q = 1;
|
||||
for (j = 1; j <= l[u]; j++)
|
||||
if (reg[j] != -1) {
|
||||
reg[j] = (reg[j] + j) % bch->n;
|
||||
q ^= bch->alpha_to[reg[j]];
|
||||
}
|
||||
if (!q) { /* store root and error
|
||||
* location number indices */
|
||||
root[count] = i;
|
||||
loc[count] = bch->n - i;
|
||||
count++;
|
||||
printf("%3d ", bch->n - i);
|
||||
}
|
||||
}
|
||||
printf("\n");
|
||||
if (count == l[u]) {
|
||||
/* no. roots = degree of elp hence <= t errors */
|
||||
for (i = 0; i < l[u]; i++)
|
||||
recd[loc[i]] ^= 1;
|
||||
return l[u];
|
||||
}
|
||||
else { /* elp has degree >t hence cannot solve */
|
||||
printf("Incomplete decoding: errors detected\n");
|
||||
return -1;
|
||||
}
|
||||
} else {
|
||||
return -1;
|
||||
}
|
||||
} else {
|
||||
return 0; // No errors
|
||||
}
|
||||
}
|
||||
|
||||
/* LEFT justified in hex */
|
||||
void bytes_to_bits(int *bytes, int *bit_dest, int num_bits) {
|
||||
for (int i = 0; i < num_bits; i++) {
|
||||
int index = i / 8;
|
||||
int bit_pos = 7 - (i % 8);
|
||||
int bit_mask = 1 << bit_pos;
|
||||
bit_dest[i] = (bytes[index] & bit_mask) != 0;
|
||||
}
|
||||
}
|
||||
|
||||
void dump_bch(bch_t *bch) {
|
||||
printf("m: %d length: %d t: %d n: %d k: %d\n", bch->m, bch->length, bch->t, bch->n, bch->k);
|
||||
}
|
||||
|
||||
#define TEST_APPLY
|
||||
|
||||
int main()
|
||||
{
|
||||
int test[][8] = {
|
||||
{ 0xb2, 0x17, 0xa2, 0xb9, 0x53, 0xdd, 0xc5, 0x52 }, /* perfect random test */
|
||||
{ 0xf0, 0x5a, 0x6a, 0x6a, 0x01, 0x63, 0x33, 0xd0 }, /* g001-cut-lenthened_457.938M.wav */
|
||||
{ 0xf0, 0x81, 0x52, 0x6b, 0x71, 0xa5, 0x63, 0x08 }, /* 1st in eotd_received_data */
|
||||
/* 3 errors */ { 0xf0, 0x85, 0x50, 0x6a, 0x01, 0xe5, 0x6e, 0x84 }, /* 2nd in eotd_received_data */
|
||||
/* fixed */ { 0xf0, 0x85, 0x50, 0x6a, 0x01, 0xe5, 0x06, 0x84 }, /* 2nd, but with the bits fixed */
|
||||
{ 0xf0, 0x85, 0x59, 0x5a, 0x01, 0xe5, 0x6e, 0x84 }, /* 3rd */
|
||||
{ 0xf1, 0x34, 0x50, 0x1a, 0x01, 0xe5, 0x66, 0xfe }, /* 4th */
|
||||
{ 0xf0, 0xeb, 0x10, 0xea, 0x01, 0x6e, 0x54, 0x1c }, /* 5th */
|
||||
{ 0xf0, 0xea, 0x5c, 0xea, 0x01, 0x6e, 0x55, 0x0e }, /* 6th */
|
||||
{ 0xe0, 0x21, 0x10, 0x1a, 0x01, 0x32, 0xbc, 0xe4 }, /* Sun Mar 20 05:41:00 2022 */
|
||||
{ 0xf0, 0x42, 0x50, 0x5b, 0xcf, 0xd5, 0x64, 0xe4 }, /* Sun Mar 20 12:58:43 2022 */
|
||||
{ 0xf0, 0x8c, 0x10, 0xaa, 0x01, 0x73, 0x7b, 0x1a }, /* Sun Mar 20 13:35:48 2022 */
|
||||
{ 0xf0, 0x8c, 0x10, 0xb1, 0xc0, 0xe0, 0x90, 0x64 }, /* Sun Mar 20 13:37:05 2022 */
|
||||
{ 0xf0, 0x8c, 0x10, 0x6a, 0x01, 0x64, 0x7a, 0xe8 }, /* Sun Mar 20 13:37:48 2022 */
|
||||
{ 0x50, 0x8c, 0x12, 0x6a, 0x01, 0x64, 0x7a, 0xe8 },
|
||||
};
|
||||
|
||||
int bits[63];
|
||||
bch_t bch;
|
||||
|
||||
bch_init(&bch, 6, 63, 3);
|
||||
|
||||
for (int count = 0; count < sizeof(test) / sizeof(*test); count++) {
|
||||
bytes_to_bits(test[count], bits, 63);
|
||||
#ifdef TEST_BYTES_TO_BITS
|
||||
printf("ORIG pkt [%d]\n", count);
|
||||
for (int i = 0; i < 8; i++) {
|
||||
printf("%02x ", test[count][i]);
|
||||
}
|
||||
printf("\n");
|
||||
|
||||
printf("ORIG pkt[%d] bits\n", count);
|
||||
for (int i = 0; i < 63; i++) {
|
||||
printf("%d ", bits[i]);
|
||||
}
|
||||
printf("\n");
|
||||
#endif
|
||||
#ifdef TEST_GENERATE
|
||||
int bch_code[18];
|
||||
generate_bch(&bch, bits, bch_code);
|
||||
printf("generated BCH\n");
|
||||
for (int i = 0; i < 18; i++) {
|
||||
printf("%d ", bch_code[i]);
|
||||
}
|
||||
printf("\n");
|
||||
#endif
|
||||
#ifdef TEST_APPLY
|
||||
int recv[63];
|
||||
// backwards, for now
|
||||
for (int i = 0; i < 45; i++) {
|
||||
recv[i + 18] = bits[i];
|
||||
}
|
||||
|
||||
for (int i = 0; i < 18; i++) {
|
||||
recv[i] = bits[i + 45];
|
||||
}
|
||||
|
||||
printf("rearranged packet: ");
|
||||
for (int i = 0; i < 63; i++) {
|
||||
printf("%d ", recv[i]);
|
||||
}
|
||||
printf("\n");
|
||||
|
||||
int corrected = apply_bch(&bch, recv);
|
||||
|
||||
printf("corrected [%d] packet: ", corrected);
|
||||
for (int i = 0; i < 63; i++) {
|
||||
printf("%d ", recv[i]);
|
||||
}
|
||||
printf("\n");
|
||||
#endif
|
||||
}
|
||||
}
|
||||
|
|
@ -0,0 +1,22 @@
|
|||
#ifndef __BCH_H
|
||||
#define __BCH_H
|
||||
|
||||
struct bch {
|
||||
int m; // 2^m - 1 is max length, n
|
||||
int length; // Actual packet size
|
||||
int n; // 2^m - 1
|
||||
int k; // Length of data portion
|
||||
int t; // Number of correctable bits
|
||||
|
||||
int *g; // Calculated polynomial of length n - k
|
||||
int *alpha_to;
|
||||
int *index_of;
|
||||
};
|
||||
|
||||
typedef struct bch bch_t;
|
||||
|
||||
int bch_init(bch_t *bch, int m, int length, int t);
|
||||
|
||||
void generate_bch(bch_t *bch, int *data, int *bb);
|
||||
|
||||
#endif
|
||||
Loading…
Reference in New Issue