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dsd-fme/src/edacs-bch3.c

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/*
* File: bch3.h
* Title: Encoder/decoder for binary BCH codes in C (Version 3.1)
* Author: Robert Morelos-Zaragoza
* Date: August 1994-June 13, 1997
* Mod: December 14, 2021, for EDACS-FM BCH Polynomial Error Generation and Detection
* Mod2: October 2022, for DSD-FME port of EDACS-FM
* Source: www.eccpage.com
*
* =============== Encoder/Decoder for binary BCH codes in C =================
*
* Version 1: Original program. The user provides the generator polynomial
* of the code (cumbersome!).
* Version 2: Computes the generator polynomial of the code.
* Version 3: No need to input the coefficients of a primitive polynomial of
* degree m, used to construct the Galois Field GF(2**m). The
* program now works for any binary BCH code of length such that:
* 2**(m-1) - 1 < length <= 2**m - 1
*
* Note: You may have to change the size of the arrays to make it work.
*
* The encoding and decoding methods used in this program are based on the
* book "Error Control Coding: Fundamentals and Applications", by Lin and
* Costello, Prentice Hall, 1983.
*
* Thanks to Patrick Boyle (pboyle@era.com) for his observation that 'bch2.c'
* did not work for lengths other than 2**m-1 which led to this new version.
* Portions of this program are from 'rs.c', a Reed-Solomon encoder/decoder
* in C, written by Simon Rockliff (simon@augean.ua.oz.au) on 21/9/89. The
* previous version of the BCH encoder/decoder in C, 'bch2.c', was written by
* Robert Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) on 5/19/92.
*
* NOTE:
* The author is not responsible for any malfunctioning of
* this program, nor for any damage caused by it. Please include the
* original program along with these comments in any redistribution.
*
* For more information, suggestions, or other ideas on implementing error
* correcting codes, please contact me at:
*
* Robert Morelos-Zaragoza
* 5120 Woodway, Suite 7036
* Houston, Texas 77056
*
* email: r.morelos-zaragoza@ieee.org
*
* COPYRIGHT NOTICE: This computer program is free for non-commercial purposes.
* You may implement this program for any non-commercial application. You may
* also implement this program for commercial purposes, provided that you
* obtain my written permission. Any modification of this program is covered
* by this copyright.
*
* == Copyright (c) 1994-7, Robert Morelos-Zaragoza. All rights reserved. ==
*
* m = order of the Galois field GF(2**m)
* n = 2**m - 1 = size of the multiplicative group of GF(2**m)
* length = length of the BCH code
* t = error correcting capability (max. no. of errors the code corrects)
* d = 2*t + 1 = designed min. distance = no. of consecutive roots of g(x) + 1
* k = n - deg(g(x)) = dimension (no. of information bits/codeword) of the code
* p[] = coefficients of a primitive polynomial used to generate GF(2**m)
* g[] = coefficients of the generator polynomial, g(x)
* alpha_to [] = log table of GF(2**m)
* index_of[] = antilog table of GF(2**m)
* ddata[] = information bits = coefficients of data polynomial, i(x)
* bb[] = coefficients of redundancy polynomial x^(length-k) i(x) modulo g(x)
* numerr = number of errors
* errpos[] = error positions
* recd[] = coefficients of the received polynomial
* decerror = number of decoding errors (in _message_ positions)
*
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
int m, n, length, k, t, d;
int p[21];
int alpha_to[1048576], index_of[1048576], g[548576];
int recd[1048576], ddata[1048576], bb[548576];
int seed;
int numerr, errpos[1024], decerror = 0;
void
read_p()
/*
* Read m, the degree of a primitive polynomial p(x) used to compute the
* Galois field GF(2**m). Get precomputed coefficients p[] of p(x). Read
* the code length.
*/
{
int i, ninf;
do {
m = 6;
} while ( !(m>1) || !(m<21) );
for (i=1; i<m; i++)
p[i] = 0;
p[0] = p[m] = 1;
if (m == 2) p[1] = 1;
else if (m == 3) p[1] = 1;
else if (m == 4) p[1] = 1;
else if (m == 5) p[2] = 1;
else if (m == 6) p[1] = 1;
else if (m == 7) p[1] = 1;
else if (m == 8) p[4] = p[5] = p[6] = 1;
else if (m == 9) p[4] = 1;
else if (m == 10) p[3] = 1;
else if (m == 11) p[2] = 1;
else if (m == 12) p[3] = p[4] = p[7] = 1;
else if (m == 13) p[1] = p[3] = p[4] = 1;
else if (m == 14) p[1] = p[11] = p[12] = 1;
else if (m == 15) p[1] = 1;
else if (m == 16) p[2] = p[3] = p[5] = 1;
else if (m == 17) p[3] = 1;
else if (m == 18) p[7] = 1;
else if (m == 19) p[1] = p[5] = p[6] = 1;
else if (m == 20) p[3] = 1;
n = 1;
for (i = 0; i <= m; i++) {
n *= 2;
}
n = n / 2 - 1;
ninf = (n + 1) / 2 - 1;
do {
length = 40;
} while ( !((length <= n)&&(length>ninf)) );
}
void
generate_gf()
/*
* Generate field GF(2**m) from the irreducible polynomial p(X) with
* coefficients 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;
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
gen_poly()
/*
* Compute the generator polynomial of a binary BCH code. Fist generate the
* cycle sets modulo 2**m - 1, cycle[][] = (i, 2*i, 4*i, ..., 2^l*i). Then
* determine those cycle sets that contain integers in the set of (d-1)
* consecutive integers {1..(d-1)}. The generator polynomial is calculated
* as the product of linear factors of the form (x+alpha^i), for every i in
* the above cycle sets.
*/
{
register int ii, jj, ll, kaux;
register int test, aux, nocycles, root, noterms, rdncy;
int cycle[1024][21], size[1024], min[1024], zeros[1024];
/* Generate cycle sets modulo n, n = 2**m - 1 */
cycle[0][0] = 0;
size[0] = 1;
cycle[1][0] = 1;
size[1] = 1;
jj = 1; /* cycle set index */
if (m > 9) {
}
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 */
t = 2;
d = 2 * t + 1;
/* Search for roots 1, 2, ..., d-1 in cycle sets */
kaux = 0;
rdncy = 0;
for (ii = 1; ii <= nocycles; ii++) {
min[kaux] = 0;
test = 0;
for (jj = 0; ((jj < size[ii]) && (!test)); jj++)
for (root = 1; ((root < d) && (!test)); root++)
if (root == cycle[ii][jj]) {
test = 1;
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++;
}
k = length - rdncy;
if (k<0)
{
exit(0);
}
/* Compute the 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];
}
}
void
encode_bch()
/*
* Compute redundacy bb[], the coefficients of b(x). The redundancy
* polynomial b(x) is the remainder after dividing x^(length-k)*ddata(x)
* by the generator polynomial g(x).
*/
{
register int i, j;
register int feedback;
for (i = 0; i < length - k; i++)
bb[i] = 0;
for (i = k - 1; i >= 0; i--) {
feedback = ddata[i] ^ bb[length - k - 1];
if (feedback != 0) {
for (j = length - k - 1; j > 0; j--)
if (g[j] != 0)
bb[j] = bb[j - 1] ^ feedback;
else
bb[j] = bb[j - 1];
bb[0] = g[0] && feedback;
} else {
for (j = length - k - 1; j > 0; j--)
bb[j] = bb[j - 1];
bb[0] = 0;
}
}
}
void
decode_bch()
/*
* Simon Rockliff's implementation of Berlekamp's algorithm.
*
* Assume we have received bits in recd[i], i=0..(n-1).
*
* Compute the 2*t syndromes by substituting alpha^i into rec(X) and
* evaluating, storing the syndromes in s[i], i=1..2t (leave s[0] zero) .
* Then we use the Berlekamp algorithm to find the error location polynomial
* elp[i].
*
* If the degree of the elp is >t, then we cannot correct all the errors, and
* we have detected an uncorrectable error pattern. We output the information
* bits uncorrected.
*
* If the degree of elp is <=t, we substitute alpha^i , i=1..n into the elp
* to get the roots, hence the inverse roots, the error location numbers.
* This step is usually called "Chien's search".
*
* If the number of errors located is not equal the degree of the elp, then
* the decoder assumes that there are more than t errors and cannot correct
* them, only detect them. We output the information bits uncorrected.
*/
{
register int i, j, u, q, t2, count = 0, syn_error = 0;
int elp[1026][1024], d[1026], l[1026], u_lu[1026], s[1025];
int root[200], loc[200], reg[201];
(void)(root);
t2 = 2 * t;
/* first form the syndromes */
for (i = 1; i <= t2; i++) {
s[i] = 0;
for (j = 0; j < length; j++)
if (recd[j] != 0)
s[i] ^= alpha_to[(i * j) % n];
if (s[i] != 0)
syn_error = 1; /* set error flag if non-zero syndrome */
/*
* Note: If the code is used only for ERROR DETECTION, then
* exit program here indicating the presence of errors.
*/
/* 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 */
/*
* Compute the error location polynomial via the Berlekamp
* iterative algorithm. Following the terminology of Lin and
* Costello's book : d[u] is the 'mu'th discrepancy, where
* u='mu'+1 and 'mu' (the Greek letter!) is the step number
* ranging from -1 to 2*t (see L&C), l[u] is the degree of
* the elp at that step, and u_l[u] is the difference between
* the step number and the degree of the elp.
*/
/* initialise table entries */
d[0] = 0; /* index form */
d[1] = s[1]; /* index form */
elp[0][0] = 0; /* index form */
elp[1][0] = 1; /* polynomial form */
for (i = 1; i < t2; i++) {
elp[0][i] = -1; /* index form */
elp[1][i] = 0; /* polynomial form */
}
l[0] = 0;
l[1] = 0;
u_lu[0] = -1;
u_lu[1] = 0;
u = 0;
do {
u++;
if (d[u] == -1) {
l[u + 1] = l[u];
for (i = 0; i <= l[u]; i++) {
elp[u + 1][i] = elp[u][i];
elp[u][i] = index_of[elp[u][i]];
}
} else
/*
* search for words with greatest u_lu[q] for
* which d[q]!=0
*/
{
q = u - 1;
while ((d[q] == -1) && (q > 0))
q--;
/* have found first non-zero d[q] */
if (q > 0) {
j = q;
do {
j--;
if ((d[j] != -1) && (u_lu[q] < u_lu[j]))
q = j;
} while (j > 0);
}
/*
* have now found q such that d[u]!=0 and
* u_lu[q] is maximum
*/
/* store degree of new elp polynomial */
if (l[u] > l[q] + u - q)
l[u + 1] = l[u];
else
l[u + 1] = l[q] + u - q;
/* form new elp(x) */
for (i = 0; i < t2; i++)
elp[u + 1][i] = 0;
for (i = 0; i <= l[q]; i++)
if (elp[q][i] != -1)
elp[u + 1][i + u - q] =
alpha_to[(d[u] + n - d[q] + elp[q][i]) % n];
for (i = 0; i <= l[u]; i++) {
elp[u + 1][i] ^= elp[u][i];
elp[u][i] = 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] = 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] ^= alpha_to[(s[u + 1 - i]
+ index_of[elp[u + 1][i]]) % n];
/* put d[u+1] into index form */
d[u + 1] = index_of[d[u + 1]];
}
} while ((u < t2) && (l[u + 1] <= t));
u++;
if (l[u] <= t) {/* Can correct errors */
/* put elp into index form */
for (i = 0; i <= l[u]; i++)
elp[u][i] = index_of[elp[u][i]];
for (i = 0; i <= l[u]; i++)
/* 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 <= n; i++) {
q = 1;
for (j = 1; j <= l[u]; j++)
if (reg[j] != -1) {
reg[j] = (reg[j] + j) % n;
q ^= alpha_to[reg[j]];
}
if (!q) { /* store root and error
* location number indices */
root[count] = i;
loc[count] = n - i;
count++;
}
}
if (count == l[u])
/* no. roots = degree of elp hence <= t errors */
for (i = 0; i < l[u]; i++)
recd[loc[i]] ^= 1;
}
}
}
//bugfix on 32-bit cygwin, probably overflowed here
unsigned long long int messagepp = 0x0;
//very simplified version, just to encode, get frame and compare
unsigned long long int edacs_bch (unsigned long long int message)
{
int i;
//not ideal to run these every frame, will want to eventually run once on start of DSD-FME, and store values
read_p(); /* Read m */
generate_gf(); /* Construct the Galois Field GF(2**m) */
gen_poly(); /* Compute the generator polynomial of BCH code */
//test shows this works, but output from program is that the poly is backwards, not sure if it corrects okay though
for (i = 0; i < k; i++){
ddata[i] = ( (message >> i) & 0x1 ); //loaded up backwards? or just outputs backwards?
}
encode_bch(); /* encode data */
/*
* recd[] are the coefficients of c(x) = x**(length-k)*data(x) + b(x)
*/
for (i = 0; i < length - k; i++)
recd[i] = bb[i];
for (i = 0; i < k; i++)
recd[i + length - k] = ddata[i];
for (i = 0; i < length; i++) {
messagepp = (messagepp << 1) | recd[39-i]; //get it in the correct direction
}
return (messagepp);
}
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