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LibrePilot/flight/libraries/rscode/berlekamp.c

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/***********************************************************************
* Copyright Henry Minsky (hqm@alum.mit.edu) 1991-2009
*
* This software library is licensed under terms of the GNU GENERAL
* PUBLIC LICENSE
*
*
* RSCODE 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 3 of the License, or
* (at your option) any later version.
*
* RSCODE 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 Rscode. If not, see <http://www.gnu.org/licenses/>.
*
* Commercial licensing is available under a separate license, please
* contact author for details.
*
* Source code is available at http://rscode.sourceforge.net
* Berlekamp-Peterson and Berlekamp-Massey Algorithms for error-location
*
* From Cain, Clark, "Error-Correction Coding For Digital Communications", pp. 205.
*
* This finds the coefficients of the error locator polynomial.
*
* The roots are then found by looking for the values of a^n
* where evaluating the polynomial yields zero.
*
* Error correction is done using the error-evaluator equation on pp 207.
*
*/
#include <stdio.h>
#include "ecc.h"
/* The Error Locator Polynomial, also known as Lambda or Sigma. Lambda[0] == 1 */
static int Lambda[MAXDEG];
/* The Error Evaluator Polynomial */
static int Omega[MAXDEG];
/* local ANSI declarations */
static int compute_discrepancy(int lambda[], int S[], int L, int n);
static void init_gamma(int gamma[]);
static void compute_modified_omega (void);
static void mul_z_poly (int src[]);
/* error locations found using Chien's search*/
static int ErrorLocs[256];
static int NErrors;
/* erasure flags */
static int ErasureLocs[256];
static int NErasures;
/* From Cain, Clark, "Error-Correction Coding For Digital Communications", pp. 216. */
void
Modified_Berlekamp_Massey (void)
{
int n, L, L2, k, d, i;
int psi[MAXDEG], psi2[MAXDEG], D[MAXDEG];
int gamma[MAXDEG];
/* initialize Gamma, the erasure locator polynomial */
init_gamma(gamma);
/* initialize to z */
copy_poly(D, gamma);
mul_z_poly(D);
copy_poly(psi, gamma);
k = -1; L = NErasures;
for (n = NErasures; n < RS_ECC_NPARITY; n++) {
d = compute_discrepancy(psi, synBytes, L, n);
if (d != 0) {
/* psi2 = psi - d*D */
for (i = 0; i < MAXDEG; i++) psi2[i] = psi[i] ^ gmult(d, D[i]);
if (L < (n-k)) {
L2 = n-k;
k = n-L;
/* D = scale_poly(ginv(d), psi); */
for (i = 0; i < MAXDEG; i++) D[i] = gmult(psi[i], ginv(d));
L = L2;
}
/* psi = psi2 */
for (i = 0; i < MAXDEG; i++) psi[i] = psi2[i];
}
mul_z_poly(D);
}
for(i = 0; i < MAXDEG; i++) Lambda[i] = psi[i];
compute_modified_omega();
}
/* given Psi (called Lambda in Modified_Berlekamp_Massey) and synBytes,
compute the combined erasure/error evaluator polynomial as
Psi*S mod z^4
*/
void
compute_modified_omega ()
{
int i;
int product[MAXDEG*2];
mult_polys(product, Lambda, synBytes);
zero_poly(Omega);
for(i = 0; i < RS_ECC_NPARITY; i++) Omega[i] = product[i];
}
/* polynomial multiplication */
void
mult_polys (int dst[], int p1[], int p2[])
{
int i, j;
int tmp1[MAXDEG*2];
for (i=0; i < (MAXDEG*2); i++) dst[i] = 0;
for (i = 0; i < MAXDEG; i++) {
for(j=MAXDEG; j<(MAXDEG*2); j++) tmp1[j]=0;
/* scale tmp1 by p1[i] */
for(j=0; j<MAXDEG; j++) tmp1[j]=gmult(p2[j], p1[i]);
/* and mult (shift) tmp1 right by i */
for (j = (MAXDEG*2)-1; j >= i; j--) tmp1[j] = tmp1[j-i];
for (j = 0; j < i; j++) tmp1[j] = 0;
/* add into partial product */
for(j=0; j < (MAXDEG*2); j++) dst[j] ^= tmp1[j];
}
}
/* gamma = product (1-z*a^Ij) for erasure locs Ij */
void
init_gamma (int gamma[])
{
int e, tmp[MAXDEG];
zero_poly(gamma);
zero_poly(tmp);
gamma[0] = 1;
for (e = 0; e < NErasures; e++) {
copy_poly(tmp, gamma);
scale_poly(gexp[ErasureLocs[e]], tmp);
mul_z_poly(tmp);
add_polys(gamma, tmp);
}
}
void
compute_next_omega (int d, int A[], int dst[], int src[])
{
int i;
for ( i = 0; i < MAXDEG; i++) {
dst[i] = src[i] ^ gmult(d, A[i]);
}
}
int
compute_discrepancy (int lambda[], int S[], int L, int n)
{
int i, sum=0;
for (i = 0; i <= L; i++)
sum ^= gmult(lambda[i], S[n-i]);
return (sum);
}
/********** polynomial arithmetic *******************/
void add_polys (int dst[], int src[])
{
int i;
for (i = 0; i < MAXDEG; i++) dst[i] ^= src[i];
}
void copy_poly (int dst[], int src[])
{
int i;
for (i = 0; i < MAXDEG; i++) dst[i] = src[i];
}
void scale_poly (int k, int poly[])
{
int i;
for (i = 0; i < MAXDEG; i++) poly[i] = gmult(k, poly[i]);
}
void zero_poly (int poly[])
{
int i;
for (i = 0; i < MAXDEG; i++) poly[i] = 0;
}
/* multiply by z, i.e., shift right by 1 */
static void mul_z_poly (int src[])
{
int i;
for (i = MAXDEG-1; i > 0; i--) src[i] = src[i-1];
src[0] = 0;
}
/* Finds all the roots of an error-locator polynomial with coefficients
* Lambda[j] by evaluating Lambda at successive values of alpha.
*
* This can be tested with the decoder's equations case.
*/
void
Find_Roots (void)
{
int sum, r, k;
NErrors = 0;
for (r = 1; r < 256; r++) {
sum = 0;
/* evaluate lambda at r */
for (k = 0; k < RS_ECC_NPARITY+1; k++) {
sum ^= gmult(gexp[(k*r)%255], Lambda[k]);
}
if (sum == 0)
{
ErrorLocs[NErrors] = (255-r); NErrors++;
//if (DEBUG) fprintf(stderr, "Root found at r = %d, (255-r) = %d\n", r, (255-r));
}
}
}
/* Combined Erasure And Error Magnitude Computation
*
* Pass in the codeword, its size in bytes, as well as
* an array of any known erasure locations, along the number
* of these erasures.
*
* Evaluate Omega(actually Psi)/Lambda' at the roots
* alpha^(-i) for error locs i.
*
* Returns 1 if everything ok, or 0 if an out-of-bounds error is found
*
*/
int
correct_errors_erasures (unsigned char codeword[],
int csize,
int nerasures,
int erasures[])
{
int r, i, j, err;
/* If you want to take advantage of erasure correction, be sure to
set NErasures and ErasureLocs[] with the locations of erasures.
*/
NErasures = nerasures;
for (i = 0; i < NErasures; i++) ErasureLocs[i] = erasures[i];
Modified_Berlekamp_Massey();
Find_Roots();
if ((NErrors <= RS_ECC_NPARITY) && NErrors > 0) {
/* first check for illegal error locs */
for (r = 0; r < NErrors; r++) {
if (ErrorLocs[r] >= csize) {
//if (DEBUG) fprintf(stderr, "Error loc i=%d outside of codeword length %d\n", i, csize);
return(0);
}
}
for (r = 0; r < NErrors; r++) {
int num, denom;
i = ErrorLocs[r];
/* evaluate Omega at alpha^(-i) */
num = 0;
for (j = 0; j < MAXDEG; j++)
num ^= gmult(Omega[j], gexp[((255-i)*j)%255]);
/* evaluate Lambda' (derivative) at alpha^(-i) ; all odd powers disappear */
denom = 0;
for (j = 1; j < MAXDEG; j += 2) {
denom ^= gmult(Lambda[j], gexp[((255-i)*(j-1)) % 255]);
}
err = gmult(num, ginv(denom));
//if (DEBUG) fprintf(stderr, "Error magnitude %#x at loc %d\n", err, csize-i);
codeword[csize-i-1] ^= err;
}
return(1);
}
else {
//if (DEBUG && NErrors) fprintf(stderr, "Uncorrectable codeword\n");
return(0);
}
}