![Bill Meier](/assets/img/avatar_default.png)
Change-Id: I8116f63ff88687c8db3fd6e8e23b22ab2f759af0 Reviewed-on: https://code.wireshark.org/review/385 Reviewed-by: Bill Meier <wmeier@newsguy.com> Tested-by: Bill Meier <wmeier@newsguy.com>
690 lines
19 KiB
C
690 lines
19 KiB
C
/* reedsolomon.c
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*
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* Reed-Solomon encoding and decoding,
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* by Phil Karn (karn@ka9q.ampr.org) September 1996
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* Copyright 1999 Phil Karn, KA9Q
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* Separate CCSDS version create Dec 1998, merged into this version May 1999
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*
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* This file is derived from my generic RS encoder/decoder, which is
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* in turn based on the program "new_rs_erasures.c" by Robert
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* Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari Thirumoorthy
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* (harit@spectra.eng.hawaii.edu), Aug 1995
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*
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* Wireshark - Network traffic analyzer
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* By Gerald Combs <gerald@wireshark.org>
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* Copyright 1998 Gerald Combs
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) 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; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
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*/
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#include <stdio.h>
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#include "reedsolomon.h"
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#ifdef CCSDS
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/* CCSDS field generator polynomial: 1+x+x^2+x^7+x^8 */
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int Pp[MM+1] = { 1, 1, 1, 0, 0, 0, 0, 1, 1 };
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#else /* not CCSDS */
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/* MM, KK, B0, PRIM are user-defined in rs.h */
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/* Primitive polynomials - see Lin & Costello, Appendix A,
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* and Lee & Messerschmitt, p. 453.
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*/
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#if(MM == 2)/* Admittedly silly */
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int Pp[MM+1] = { 1, 1, 1 };
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#elif(MM == 3)
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/* 1 + x + x^3 */
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int Pp[MM+1] = { 1, 1, 0, 1 };
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#elif(MM == 4)
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/* 1 + x + x^4 */
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int Pp[MM+1] = { 1, 1, 0, 0, 1 };
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#elif(MM == 5)
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/* 1 + x^2 + x^5 */
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int Pp[MM+1] = { 1, 0, 1, 0, 0, 1 };
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#elif(MM == 6)
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/* 1 + x + x^6 */
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1 };
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#elif(MM == 7)
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/* 1 + x^3 + x^7 */
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int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 1 };
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#elif(MM == 8)
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/* 1+x^2+x^3+x^4+x^8 */
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int Pp[MM+1] = { 1, 0, 1, 1, 1, 0, 0, 0, 1 };
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#elif(MM == 9)
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/* 1+x^4+x^9 */
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int Pp[MM+1] = { 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
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#elif(MM == 10)
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/* 1+x^3+x^10 */
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int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 11)
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/* 1+x^2+x^11 */
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int Pp[MM+1] = { 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 12)
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/* 1+x+x^4+x^6+x^12 */
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int Pp[MM+1] = { 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 13)
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/* 1+x+x^3+x^4+x^13 */
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int Pp[MM+1] = { 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 14)
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/* 1+x+x^6+x^10+x^14 */
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 };
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#elif(MM == 15)
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/* 1+x+x^15 */
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int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
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#elif(MM == 16)
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/* 1+x+x^3+x^12+x^16 */
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int Pp[MM+1] = { 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 };
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#else
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#error "Either CCSDS must be defined, or MM must be set in range 2-16"
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#endif
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#endif
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#ifdef STANDARD_ORDER /* first byte transmitted is index of x**(KK-1) in message poly*/
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/* definitions used in the encode routine*/
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#define MESSAGE(i) data[KK-(i)-1]
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#define REMAINDER(i) bb[NN-KK-(i)-1]
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/* definitions used in the decode routine*/
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#define RECEIVED(i) data[NN-1-(i)]
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#define ERAS_INDEX(i) (NN-1-eras_pos[i])
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#define INDEX_TO_POS(i) (NN-1-(i))
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#else /* first byte transmitted is index of x**0 in message polynomial*/
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/* definitions used in the encode routine*/
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#define MESSAGE(i) data[i]
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#define REMAINDER(i) bb[i]
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/* definitions used in the decode routine*/
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#define RECEIVED(i) data[i]
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#define ERAS_INDEX(i) eras_pos[i]
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#define INDEX_TO_POS(i) i
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#endif
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/* This defines the type used to store an element of the Galois Field
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* used by the code. Make sure this is something larger than a char if
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* if anything larger than GF(256) is used.
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*
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* Note: unsigned char will work up to GF(256) but int seems to run
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* faster on the Pentium.
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*/
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typedef int gf;
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/* index->polynomial form conversion table */
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static gf Alpha_to[NN + 1];
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/* Polynomial->index form conversion table */
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static gf Index_of[NN + 1];
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/* No legal value in index form represents zero, so
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* we need a special value for this purpose
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*/
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#define A0 (NN)
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/* Generator polynomial g(x) in index form */
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static gf Gg[NN - KK + 1];
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static int RS_init; /* Initialization flag */
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/* Compute x % NN, where NN is 2**MM - 1,
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* without a slow divide
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*/
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/* static inline gf*/
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static gf
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modnn(int x)
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{
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while (x >= NN) {
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x -= NN;
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x = (x >> MM) + (x & NN);
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}
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return x;
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}
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#define min_(a,b) ((a) < (b) ? (a) : (b))
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#define CLEAR(a,n) {\
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int ci;\
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for(ci=(n)-1;ci >=0;ci--)\
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(a)[ci] = 0;\
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}
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#define COPY(a,b,n) {\
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int ci;\
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for(ci=(n)-1;ci >=0;ci--)\
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(a)[ci] = (b)[ci];\
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}
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#define COPYDOWN(a,b,n) {\
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int ci;\
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for(ci=(n)-1;ci >=0;ci--)\
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(a)[ci] = (b)[ci];\
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}
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static void init_rs(void);
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#ifdef CCSDS
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/* Conversion lookup tables from conventional alpha to Berlekamp's
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* dual-basis representation. Used in the CCSDS version only.
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* taltab[] -- convert conventional to dual basis
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* tal1tab[] -- convert dual basis to conventional
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* Note: the actual RS encoder/decoder works with the conventional basis.
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* So data is converted from dual to conventional basis before either
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* encoding or decoding and then converted back.
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*/
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static unsigned char taltab[NN+1],tal1tab[NN+1];
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static unsigned char tal[] = { 0x8d, 0xef, 0xec, 0x86, 0xfa, 0x99, 0xaf, 0x7b };
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/* Generate conversion lookup tables between conventional alpha representation
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* (@**7, @**6, ...@**0)
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* and Berlekamp's dual basis representation
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* (l0, l1, ...l7)
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*/
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static void
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gen_ltab(void)
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{
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int i,j,k;
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for(i=0;i<256;i++){/* For each value of input */
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taltab[i] = 0;
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for(j=0;j<8;j++) /* for each column of matrix */
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for(k=0;k<8;k++){ /* for each row of matrix */
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if(i & (1<<k))
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taltab[i] ^= tal[7-k] & (1<<j);
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}
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tal1tab[taltab[i]] = i;
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}
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}
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#endif /* CCSDS */
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#if PRIM != 1
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static int Ldec;/* Decrement for aux location variable in Chien search */
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static void
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gen_ldec(void)
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{
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for(Ldec=1;(Ldec % PRIM) != 0;Ldec+= NN)
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;
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Ldec /= PRIM;
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}
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#else
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#define Ldec 1
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#endif
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/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[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
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alpha=2 is the primitive element of GF(2**m)
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HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
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Let @ represent the primitive element commonly called "alpha" that
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is the root of the primitive polynomial p(x). Then in GF(2^m), for any
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0 <= i <= 2^m-2,
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@^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
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where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
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of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
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example the polynomial representation of @^5 would be given by the binary
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representation of the integer "alpha_to[5]".
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Similarily, index_of[] can be used as follows:
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As above, let @ represent the primitive element of GF(2^m) that is
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the root of the primitive polynomial p(x). In order to find the power
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of @ (alpha) that has the polynomial representation
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a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
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we consider the integer "i" whose binary representation with a(0) being LSB
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and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
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"index_of[i]". Now, @^index_of[i] is that element whose polynomial
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representation is (a(0),a(1),a(2),...,a(m-1)).
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NOTE:
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The element alpha_to[2^m-1] = 0 always signifying that the
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representation of "@^infinity" = 0 is (0,0,0,...,0).
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Similarily, the element index_of[0] = A0 always signifying
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that the power of alpha which has the polynomial representation
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(0,0,...,0) is "infinity".
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*/
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static void
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generate_gf(void)
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{
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register int i, mask;
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mask = 1;
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Alpha_to[MM] = 0;
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for (i = 0; i < MM; i++) {
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Alpha_to[i] = mask;
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Index_of[Alpha_to[i]] = i;
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/* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
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if (Pp[i] != 0)
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Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
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mask <<= 1; /* single left-shift */
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}
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Index_of[Alpha_to[MM]] = MM;
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/*
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* Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
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* poly-repr of @^i shifted left one-bit and accounting for any @^MM
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* term that may occur when poly-repr of @^i is shifted.
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*/
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mask >>= 1;
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for (i = MM + 1; i < NN; i++) {
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if (Alpha_to[i - 1] >= mask)
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Alpha_to[i] = Alpha_to[MM] ^ ((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] = A0;
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Alpha_to[NN] = 0;
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}
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/*
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* Obtain the generator polynomial of the TT-error correcting, length
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* NN=(2**MM -1) Reed Solomon code from the product of (X+@**(B0+i)), i = 0,
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* ... ,(2*TT-1)
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*
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* Examples:
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*
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* If B0 = 1, TT = 1. deg(g(x)) = 2*TT = 2.
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* g(x) = (x+@) (x+@**2)
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*
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* If B0 = 0, TT = 2. deg(g(x)) = 2*TT = 4.
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* g(x) = (x+1) (x+@) (x+@**2) (x+@**3)
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*/
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static void
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gen_poly(void)
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{
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register int i, j;
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Gg[0] = 1;
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for (i = 0; i < NN - KK; i++) {
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Gg[i+1] = 1;
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/*
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* Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
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* (@**(B0+i)*PRIM + x)
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*/
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for (j = i; j > 0; j--)
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if (Gg[j] != 0)
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Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + (B0 + i) *PRIM)];
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else
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Gg[j] = Gg[j - 1];
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/* Gg[0] can never be zero */
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Gg[0] = Alpha_to[modnn(Index_of[Gg[0]] + (B0 + i) * PRIM)];
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}
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/* convert Gg[] to index form for quicker encoding */
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for (i = 0; i <= NN - KK; i++)
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Gg[i] = Index_of[Gg[i]];
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}
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/*
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* take the string of symbols in data[i], i=0..(k-1) and encode
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* systematically to produce NN-KK parity symbols in bb[0]..bb[NN-KK-1] data[]
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* is input and bb[] is output in polynomial form. Encoding is done by using
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* a feedback shift register with appropriate connections specified by the
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* elements of Gg[], which was generated above. Codeword is c(X) =
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* data(X)*X**(NN-KK)+ b(X)
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*/
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int
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encode_rs(dtype data[KK], dtype bb[NN-KK])
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{
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register int i, j;
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gf feedback;
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#if DEBUG >= 1 && MM != 8
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/* Check for illegal input values */
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for(i=0;i<KK;i++)
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if(MESSAGE(i) > NN)
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return -1;
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#endif
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if(!RS_init)
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init_rs();
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CLEAR(bb,NN-KK);
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#ifdef CCSDS
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/* Convert to conventional basis */
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for(i=0;i<KK;i++)
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MESSAGE(i) = tal1tab[MESSAGE(i)];
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#endif
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for(i = KK - 1; i >= 0; i--) {
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feedback = Index_of[MESSAGE(i) ^ REMAINDER(NN - KK - 1)];
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if (feedback != A0) { /* feedback term is non-zero */
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for (j = NN - KK - 1; j > 0; j--)
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if (Gg[j] != A0)
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REMAINDER(j) = REMAINDER(j - 1) ^ Alpha_to[modnn(Gg[j] + feedback)];
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else
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REMAINDER(j) = REMAINDER(j - 1);
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REMAINDER(0) = Alpha_to[modnn(Gg[0] + feedback)];
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} else { /* feedback term is zero. encoder becomes a
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* single-byte shifter */
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for (j = NN - KK - 1; j > 0; j--)
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REMAINDER(j) = REMAINDER(j - 1);
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REMAINDER(0) = 0;
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}
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}
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#ifdef CCSDS
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/* Convert to l-basis */
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for(i=0;i<NN;i++)
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MESSAGE(i) = taltab[MESSAGE(i)];
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#endif
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return 0;
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}
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/*
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* Performs ERRORS+ERASURES decoding of RS codes. If decoding is successful,
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* writes the codeword into data[] itself. Otherwise data[] is unaltered.
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*
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* Return number of symbols corrected, or -1 if codeword is illegal
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* or uncorrectable. If eras_pos is non-null, the detected error locations
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* are written back. NOTE! This array must be at least NN-KK elements long.
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*
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* First "no_eras" erasures are declared by the calling program. Then, the
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* maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
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* If the number of channel errors is not greater than "t_after_eras" the
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* transmitted codeword will be recovered. Details of algorithm can be found
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* in R. Blahut's "Theory ... of Error-Correcting Codes".
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* Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
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* will result. The decoder *could* check for this condition, but it would involve
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* extra time on every decoding operation.
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*/
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int
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eras_dec_rs(dtype data[NN], int eras_pos[NN-KK], int no_eras)
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{
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int deg_lambda, el, deg_omega;
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int i, j, r,k;
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gf u,q,tmp,num1,num2,den,discr_r;
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gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
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* and syndrome poly */
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gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
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gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
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int syn_error, count;
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if(!RS_init)
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init_rs();
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#ifdef CCSDS
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/* Convert to conventional basis */
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for(i=0;i<NN;i++)
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RECEIVED(i) = tal1tab[RECEIVED(i)];
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#endif
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#if DEBUG >= 1 && MM != 8
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/* Check for illegal input values */
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for(i=0;i<NN;i++)
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if(RECEIVED(i) > NN)
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return -1;
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#endif
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/* form the syndromes; i.e., evaluate data(x) at roots of g(x)
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* namely @**(B0+i)*PRIM, i = 0, ... ,(NN-KK-1)
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*/
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for(i=1;i<=NN-KK;i++){
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s[i] = RECEIVED(0);
|
|
}
|
|
for(j=1;j<NN;j++){
|
|
if(RECEIVED(j) == 0)
|
|
continue;
|
|
tmp = Index_of[RECEIVED(j)];
|
|
|
|
/* s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*j)]; */
|
|
for(i=1;i<=NN-KK;i++)
|
|
s[i] ^= Alpha_to[modnn(tmp + (B0+i-1)*PRIM*j)];
|
|
}
|
|
/* Convert syndromes to index form, checking for nonzero condition */
|
|
syn_error = 0;
|
|
for(i=1;i<=NN-KK;i++){
|
|
syn_error |= s[i];
|
|
/*printf("syndrome %d = %x\n",i,s[i]);*/
|
|
s[i] = Index_of[s[i]];
|
|
}
|
|
|
|
if (!syn_error) {
|
|
/* if syndrome is zero, data[] is a codeword and there are no
|
|
* errors to correct. So return data[] unmodified
|
|
*/
|
|
count = 0;
|
|
goto finish;
|
|
}
|
|
CLEAR(&lambda[1],NN-KK);
|
|
lambda[0] = 1;
|
|
|
|
if (no_eras > 0) {
|
|
/* Init lambda to be the erasure locator polynomial */
|
|
lambda[1] = Alpha_to[modnn(PRIM * ERAS_INDEX(0))];
|
|
for (i = 1; i < no_eras; i++) {
|
|
u = modnn(PRIM*ERAS_INDEX(i));
|
|
for (j = i+1; j > 0; j--) {
|
|
tmp = Index_of[lambda[j - 1]];
|
|
if(tmp != A0)
|
|
lambda[j] ^= Alpha_to[modnn(u + tmp)];
|
|
}
|
|
}
|
|
#if DEBUG >= 1
|
|
/* Test code that verifies the erasure locator polynomial just constructed
|
|
Needed only for decoder debugging. */
|
|
|
|
/* find roots of the erasure location polynomial */
|
|
for(i=1;i<=no_eras;i++)
|
|
reg[i] = Index_of[lambda[i]];
|
|
count = 0;
|
|
for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
|
|
q = 1;
|
|
for (j = 1; j <= no_eras; j++)
|
|
if (reg[j] != A0) {
|
|
reg[j] = modnn(reg[j] + j);
|
|
q ^= Alpha_to[reg[j]];
|
|
}
|
|
if (q != 0)
|
|
continue;
|
|
/* store root and error location number indices */
|
|
root[count] = i;
|
|
loc[count] = k;
|
|
count++;
|
|
}
|
|
if (count != no_eras) {
|
|
printf("\n lambda(x) is WRONG\n");
|
|
count = -1;
|
|
goto finish;
|
|
}
|
|
#if DEBUG >= 2
|
|
printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
|
|
for (i = 0; i < count; i++)
|
|
printf("%d ", loc[i]);
|
|
printf("\n");
|
|
#endif
|
|
#endif
|
|
}
|
|
for(i=0;i<NN-KK+1;i++)
|
|
b[i] = Index_of[lambda[i]];
|
|
|
|
/*
|
|
* Begin Berlekamp-Massey algorithm to determine error+erasure
|
|
* locator polynomial
|
|
*/
|
|
r = no_eras;
|
|
el = no_eras;
|
|
while (++r <= NN-KK) { /* r is the step number */
|
|
/* Compute discrepancy at the r-th step in poly-form */
|
|
discr_r = 0;
|
|
for (i = 0; i < r; i++){
|
|
if ((lambda[i] != 0) && (s[r - i] != A0)) {
|
|
discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
|
|
}
|
|
}
|
|
discr_r = Index_of[discr_r]; /* Index form */
|
|
if (discr_r == A0) {
|
|
/* 2 lines below: B(x) <-- x*B(x) */
|
|
COPYDOWN(&b[1],b,NN-KK);
|
|
b[0] = A0;
|
|
} else {
|
|
/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
|
|
t[0] = lambda[0];
|
|
for (i = 0 ; i < NN-KK; i++) {
|
|
if(b[i] != A0)
|
|
t[i+1] = lambda[i+1] ^ Alpha_to[modnn(discr_r + b[i])];
|
|
else
|
|
t[i+1] = lambda[i+1];
|
|
}
|
|
if (2 * el <= r + no_eras - 1) {
|
|
el = r + no_eras - el;
|
|
/*
|
|
* 2 lines below: B(x) <-- inv(discr_r) *
|
|
* lambda(x)
|
|
*/
|
|
for (i = 0; i <= NN-KK; i++)
|
|
b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
|
|
} else {
|
|
/* 2 lines below: B(x) <-- x*B(x) */
|
|
COPYDOWN(&b[1],b,NN-KK);
|
|
b[0] = A0;
|
|
}
|
|
COPY(lambda,t,NN-KK+1);
|
|
}
|
|
}
|
|
|
|
/* Convert lambda to index form and compute deg(lambda(x)) */
|
|
deg_lambda = 0;
|
|
for(i=0;i<NN-KK+1;i++){
|
|
lambda[i] = Index_of[lambda[i]];
|
|
if(lambda[i] != A0)
|
|
deg_lambda = i;
|
|
}
|
|
/*
|
|
* Find roots of the error+erasure locator polynomial by Chien
|
|
* Search
|
|
*/
|
|
COPY(®[1],&lambda[1],NN-KK);
|
|
count = 0; /* Number of roots of lambda(x) */
|
|
for (i = 1,k=NN-Ldec; i <= NN; i++,k = modnn(NN+k-Ldec)) {
|
|
q = 1;
|
|
for (j = deg_lambda; j > 0; j--){
|
|
if (reg[j] != A0) {
|
|
reg[j] = modnn(reg[j] + j);
|
|
q ^= Alpha_to[reg[j]];
|
|
}
|
|
}
|
|
if (q != 0)
|
|
continue;
|
|
/* store root (index-form) and error location number */
|
|
root[count] = i;
|
|
loc[count] = k;
|
|
/* If we've already found max possible roots,
|
|
* abort the search to save time
|
|
*/
|
|
if(++count == deg_lambda)
|
|
break;
|
|
}
|
|
if (deg_lambda != count) {
|
|
/*
|
|
* deg(lambda) unequal to number of roots => uncorrectable
|
|
* error detected
|
|
*/
|
|
count = -1;
|
|
goto finish;
|
|
}
|
|
/*
|
|
* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
|
|
* x**(NN-KK)). in index form. Also find deg(omega).
|
|
*/
|
|
deg_omega = 0;
|
|
for (i = 0; i < NN-KK;i++){
|
|
tmp = 0;
|
|
j = (deg_lambda < i) ? deg_lambda : i;
|
|
for(;j >= 0; j--){
|
|
if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
|
|
tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
|
|
}
|
|
if(tmp != 0)
|
|
deg_omega = i;
|
|
omega[i] = Index_of[tmp];
|
|
}
|
|
omega[NN-KK] = A0;
|
|
|
|
/*
|
|
* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
|
|
* inv(X(l))**(B0-1) and den = lambda_pr(inv(X(l))) all in poly-form
|
|
*/
|
|
for (j = count-1; j >=0; j--) {
|
|
num1 = 0;
|
|
for (i = deg_omega; i >= 0; i--) {
|
|
if (omega[i] != A0)
|
|
num1 ^= Alpha_to[modnn(omega[i] + i * root[j])];
|
|
}
|
|
num2 = Alpha_to[modnn(root[j] * (B0 - 1) + NN)];
|
|
den = 0;
|
|
|
|
/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
|
|
for (i = min_(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
|
|
if(lambda[i+1] != A0)
|
|
den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
|
|
}
|
|
if (den == 0) {
|
|
#if DEBUG >= 1
|
|
printf("\n ERROR: denominator = 0\n");
|
|
#endif
|
|
/* Convert to dual- basis */
|
|
count = -1;
|
|
goto finish;
|
|
}
|
|
/* Apply error to data */
|
|
if (num1 != 0) {
|
|
RECEIVED(loc[j]) ^= Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
|
|
}
|
|
}
|
|
finish:
|
|
#ifdef CCSDS
|
|
/* Convert to dual- basis */
|
|
for(i=0;i<NN;i++)
|
|
RECEIVED(i) = taltab[RECEIVED(i)];
|
|
#endif
|
|
if(eras_pos != NULL){
|
|
for(i=0;i<count;i++){
|
|
if(eras_pos!= NULL)
|
|
eras_pos[i] = INDEX_TO_POS(loc[i]);
|
|
}
|
|
}
|
|
return count;
|
|
}
|
|
/* Encoder/decoder initialization - call this first! */
|
|
static void
|
|
init_rs(void)
|
|
{
|
|
generate_gf();
|
|
gen_poly();
|
|
#ifdef CCSDS
|
|
gen_ltab();
|
|
#endif
|
|
#if PRIM != 1
|
|
gen_ldec();
|
|
#endif
|
|
RS_init = 1;
|
|
}
|