- /*
- * The copyright in this software is being made available under the 2-clauses
- * BSD License, included below. This software may be subject to other third
- * party and contributor rights, including patent rights, and no such rights
- * are granted under this license.
- *
- * Copyright (c) 2001-2003, David Janssens
- * Copyright (c) 2002-2003, Yannick Verschueren
- * Copyright (c) 2003-2005, Francois Devaux and Antonin Descampe
- * Copyright (c) 2005, Herve Drolon, FreeImage Team
- * Copyright (c) 2002-2005, Communications and remote sensing Laboratory, Universite catholique de Louvain, Belgium
- * Copyright (c) 2005-2006, Dept. of Electronic and Information Engineering, Universita' degli Studi di Perugia, Italy
- * All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
- * 2. Redistributions in binary form must reproduce the above copyright
- * notice, this list of conditions and the following disclaimer in the
- * documentation and/or other materials provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS `AS IS'
- * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
- * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
- * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
- * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
- * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
- * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
- * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
- * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
- * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
- * POSSIBILITY OF SUCH DAMAGE.
- */
+/*
+* The copyright in this software is being made available under the 2-clauses
+* BSD License, included below. This software may be subject to other third
+* party and contributor rights, including patent rights, and no such rights
+* are granted under this license.
+*
+* Copyright (c) 2001-2003, David Janssens
+* Copyright (c) 2002-2003, Yannick Verschueren
+* Copyright (c) 2003-2005, Francois Devaux and Antonin Descampe
+* Copyright (c) 2005, Herve Drolon, FreeImage Team
+* Copyright (c) 2002-2005, Communications and remote sensing Laboratory, Universite catholique de Louvain, Belgium
+* Copyright (c) 2005-2006, Dept. of Electronic and Information Engineering, Universita' degli Studi di Perugia, Italy
+* All rights reserved.
+*
+* Redistribution and use in source and binary forms, with or without
+* modification, are permitted provided that the following conditions
+* are met:
+* 1. Redistributions of source code must retain the above copyright
+* notice, this list of conditions and the following disclaimer.
+* 2. Redistributions in binary form must reproduce the above copyright
+* notice, this list of conditions and the following disclaimer in the
+* documentation and/or other materials provided with the distribution.
+*
+* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS `AS IS'
+* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+* POSSIBILITY OF SUCH DAMAGE.
+*/
#ifdef USE_JPWL
/**
* Reed-Solomon coding and decoding
* Phil Karn (karn@ka9q.ampr.org) September 1996
- *
+ *
* This file is derived from the program "new_rs_erasures.c" by Robert
* Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari Thirumoorthy
* (harit@spectra.eng.hawaii.edu), Aug 1995
typedef int gf;
/* KK = number of information symbols */
-static int KK;
+static int KK;
/* Primitive polynomials - see Lin & Costello, Appendix A,
* and Lee & Messerschmitt, p. 453.
*/
#if(MM == 2)/* Admittedly silly */
-int Pp[MM+1] = { 1, 1, 1 };
+int Pp[MM + 1] = { 1, 1, 1 };
#elif(MM == 3)
/* 1 + x + x^3 */
-int Pp[MM+1] = { 1, 1, 0, 1 };
+int Pp[MM + 1] = { 1, 1, 0, 1 };
#elif(MM == 4)
/* 1 + x + x^4 */
-int Pp[MM+1] = { 1, 1, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 1, 0, 0, 1 };
#elif(MM == 5)
/* 1 + x^2 + x^5 */
-int Pp[MM+1] = { 1, 0, 1, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 0, 1, 0, 0, 1 };
#elif(MM == 6)
/* 1 + x + x^6 */
-int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 1, 0, 0, 0, 0, 1 };
#elif(MM == 7)
/* 1 + x^3 + x^7 */
-int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 0, 0, 1, 0, 0, 0, 1 };
#elif(MM == 8)
/* 1+x^2+x^3+x^4+x^8 */
-int Pp[MM+1] = { 1, 0, 1, 1, 1, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 0, 1, 1, 1, 0, 0, 0, 1 };
#elif(MM == 9)
/* 1+x^4+x^9 */
-int Pp[MM+1] = { 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
#elif(MM == 10)
/* 1+x^3+x^10 */
-int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 };
#elif(MM == 11)
/* 1+x^2+x^11 */
-int Pp[MM+1] = { 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
#elif(MM == 12)
/* 1+x+x^4+x^6+x^12 */
-int Pp[MM+1] = { 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1 };
#elif(MM == 13)
/* 1+x+x^3+x^4+x^13 */
-int Pp[MM+1] = { 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
#elif(MM == 14)
/* 1+x+x^6+x^10+x^14 */
-int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 };
#elif(MM == 15)
/* 1+x+x^15 */
-int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 };
#elif(MM == 16)
/* 1+x+x^3+x^12+x^16 */
-int Pp[MM+1] = { 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 };
+int Pp[MM + 1] = { 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 };
#else
#error "MM must be in range 2-16"
#endif
/* Alpha exponent for the first root of the generator polynomial */
-#define B0 0 /* Different from the default 1 */
+#define B0 0 /* Different from the default 1 */
/* index->polynomial form conversion table */
gf Alpha_to[NN + 1];
/* No legal value in index form represents zero, so
* we need a special value for this purpose
*/
-#define A0 (NN)
+#define A0 (NN)
/* Generator polynomial g(x)
* Degree of g(x) = 2*TT
* has roots @**B0, @**(B0+1), ... ,@^(B0+2*TT-1)
*/
/*gf Gg[NN - KK + 1];*/
-gf Gg[NN - 1];
+gf Gg[NN - 1];
/* Compute x % NN, where NN is 2**MM - 1,
* without a slow divide
static /*inline*/ gf
modnn(int x)
{
- while (x >= NN) {
- x -= NN;
- x = (x >> MM) + (x & NN);
- }
- return x;
+ while (x >= NN) {
+ x -= NN;
+ x = (x >> MM) + (x & NN);
+ }
+ return x;
}
-/*#define min(a,b) ((a) < (b) ? (a) : (b))*/
-
-#define CLEAR(a,n) {\
- int ci;\
- for(ci=(n)-1;ci >=0;ci--)\
- (a)[ci] = 0;\
- }
-
-#define COPY(a,b,n) {\
- int ci;\
- for(ci=(n)-1;ci >=0;ci--)\
- (a)[ci] = (b)[ci];\
- }
-#define COPYDOWN(a,b,n) {\
- int ci;\
- for(ci=(n)-1;ci >=0;ci--)\
- (a)[ci] = (b)[ci];\
- }
+/*#define min(a,b) ((a) < (b) ? (a) : (b))*/
+
+#define CLEAR(a,n) {\
+ int ci;\
+ for(ci=(n)-1;ci >=0;ci--)\
+ (a)[ci] = 0;\
+ }
+
+#define COPY(a,b,n) {\
+ int ci;\
+ for(ci=(n)-1;ci >=0;ci--)\
+ (a)[ci] = (b)[ci];\
+ }
+#define COPYDOWN(a,b,n) {\
+ int ci;\
+ for(ci=(n)-1;ci >=0;ci--)\
+ (a)[ci] = (b)[ci];\
+ }
void init_rs(int k)
{
- KK = k;
- if (KK >= NN) {
- printf("KK must be less than 2**MM - 1\n");
- exit(1);
- }
-
- generate_gf();
- gen_poly();
+ KK = k;
+ if (KK >= NN) {
+ printf("KK must be less than 2**MM - 1\n");
+ exit(1);
+ }
+
+ generate_gf();
+ gen_poly();
}
/* generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m]
a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
we consider the integer "i" whose binary representation with a(0) being LSB
and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry
- "index_of[i]". Now, @^index_of[i] is that element whose polynomial
+ "index_of[i]". Now, @^index_of[i] is that element whose polynomial
representation is (a(0),a(1),a(2),...,a(m-1)).
NOTE:
The element alpha_to[2^m-1] = 0 always signifying that the
Similarly, the element index_of[0] = A0 always signifying
that the power of alpha which has the polynomial representation
(0,0,...,0) is "infinity".
-
+
*/
void
generate_gf(void)
{
- register int i, mask;
-
- mask = 1;
- Alpha_to[MM] = 0;
- for (i = 0; i < MM; i++) {
- Alpha_to[i] = mask;
- Index_of[Alpha_to[i]] = i;
- /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
- if (Pp[i] != 0)
- Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
- mask <<= 1; /* single left-shift */
- }
- Index_of[Alpha_to[MM]] = MM;
- /*
- * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
- * poly-repr of @^i shifted left one-bit and accounting for any @^MM
- * term that may occur when poly-repr of @^i is shifted.
- */
- mask >>= 1;
- for (i = MM + 1; i < NN; i++) {
- if (Alpha_to[i - 1] >= mask)
- Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
- else
- Alpha_to[i] = Alpha_to[i - 1] << 1;
- Index_of[Alpha_to[i]] = i;
- }
- Index_of[0] = A0;
- Alpha_to[NN] = 0;
+ register int i, mask;
+
+ mask = 1;
+ Alpha_to[MM] = 0;
+ for (i = 0; i < MM; i++) {
+ Alpha_to[i] = mask;
+ Index_of[Alpha_to[i]] = i;
+ /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */
+ if (Pp[i] != 0) {
+ Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */
+ }
+ mask <<= 1; /* single left-shift */
+ }
+ Index_of[Alpha_to[MM]] = MM;
+ /*
+ * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by
+ * poly-repr of @^i shifted left one-bit and accounting for any @^MM
+ * term that may occur when poly-repr of @^i is shifted.
+ */
+ mask >>= 1;
+ for (i = MM + 1; i < NN; i++) {
+ if (Alpha_to[i - 1] >= mask) {
+ Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1);
+ } else {
+ Alpha_to[i] = Alpha_to[i - 1] << 1;
+ }
+ Index_of[Alpha_to[i]] = i;
+ }
+ Index_of[0] = A0;
+ Alpha_to[NN] = 0;
}
void
gen_poly(void)
{
- register int i, j;
-
- Gg[0] = Alpha_to[B0];
- Gg[1] = 1; /* g(x) = (X+@**B0) initially */
- for (i = 2; i <= NN - KK; i++) {
- Gg[i] = 1;
- /*
- * Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
- * (@**(B0+i-1) + x)
- */
- for (j = i - 1; j > 0; j--)
- if (Gg[j] != 0)
- Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + B0 + i - 1)];
- else
- Gg[j] = Gg[j - 1];
- /* Gg[0] can never be zero */
- Gg[0] = Alpha_to[modnn((Index_of[Gg[0]]) + B0 + i - 1)];
- }
- /* convert Gg[] to index form for quicker encoding */
- for (i = 0; i <= NN - KK; i++)
- Gg[i] = Index_of[Gg[i]];
+ register int i, j;
+
+ Gg[0] = Alpha_to[B0];
+ Gg[1] = 1; /* g(x) = (X+@**B0) initially */
+ for (i = 2; i <= NN - KK; i++) {
+ Gg[i] = 1;
+ /*
+ * Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
+ * (@**(B0+i-1) + x)
+ */
+ for (j = i - 1; j > 0; j--)
+ if (Gg[j] != 0) {
+ Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + B0 + i - 1)];
+ } else {
+ Gg[j] = Gg[j - 1];
+ }
+ /* Gg[0] can never be zero */
+ Gg[0] = Alpha_to[modnn((Index_of[Gg[0]]) + B0 + i - 1)];
+ }
+ /* convert Gg[] to index form for quicker encoding */
+ for (i = 0; i <= NN - KK; i++) {
+ Gg[i] = Index_of[Gg[i]];
+ }
}
int
encode_rs(dtype *data, dtype *bb)
{
- register int i, j;
- gf feedback;
+ register int i, j;
+ gf feedback;
- CLEAR(bb,NN-KK);
- for (i = KK - 1; i >= 0; i--) {
+ CLEAR(bb, NN - KK);
+ for (i = KK - 1; i >= 0; i--) {
#if (MM != 8)
- if(data[i] > NN)
- return -1; /* Illegal symbol */
+ if (data[i] > NN) {
+ return -1; /* Illegal symbol */
+ }
#endif
- feedback = Index_of[data[i] ^ bb[NN - KK - 1]];
- if (feedback != A0) { /* feedback term is non-zero */
- for (j = NN - KK - 1; j > 0; j--)
- if (Gg[j] != A0)
- bb[j] = bb[j - 1] ^ Alpha_to[modnn(Gg[j] + feedback)];
- else
- bb[j] = bb[j - 1];
- bb[0] = Alpha_to[modnn(Gg[0] + feedback)];
- } else { /* feedback term is zero. encoder becomes a
- * single-byte shifter */
- for (j = NN - KK - 1; j > 0; j--)
- bb[j] = bb[j - 1];
- bb[0] = 0;
- }
- }
- return 0;
+ feedback = Index_of[data[i] ^ bb[NN - KK - 1]];
+ if (feedback != A0) { /* feedback term is non-zero */
+ for (j = NN - KK - 1; j > 0; j--)
+ if (Gg[j] != A0) {
+ bb[j] = bb[j - 1] ^ Alpha_to[modnn(Gg[j] + feedback)];
+ } else {
+ bb[j] = bb[j - 1];
+ }
+ bb[0] = Alpha_to[modnn(Gg[0] + feedback)];
+ } else {
+ /* feedback term is zero. encoder becomes a
+ * single-byte shifter */
+ for (j = NN - KK - 1; j > 0; j--) {
+ bb[j] = bb[j - 1];
+ }
+ bb[0] = 0;
+ }
+ }
+ return 0;
}
/*
*
* Return number of symbols corrected, or -1 if codeword is illegal
* or uncorrectable.
- *
+ *
* First "no_eras" erasures are declared by the calling program. Then, the
* maximum # of errors correctable is t_after_eras = floor((NN-KK-no_eras)/2).
* If the number of channel errors is not greater than "t_after_eras" the
int
eras_dec_rs(dtype *data, int *eras_pos, int no_eras)
{
- int deg_lambda, el, deg_omega;
- int i, j, r;
- gf u,q,tmp,num1,num2,den,discr_r;
- gf recd[NN];
- /* Err+Eras Locator poly and syndrome poly */
- /*gf lambda[NN-KK + 1], s[NN-KK + 1];
- gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
- gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];*/
- gf lambda[NN + 1], s[NN + 1];
- gf b[NN + 1], t[NN + 1], omega[NN + 1];
- gf root[NN], reg[NN + 1], loc[NN];
- int syn_error, count;
-
- /* data[] is in polynomial form, copy and convert to index form */
- for (i = NN-1; i >= 0; i--){
+ int deg_lambda, el, deg_omega;
+ int i, j, r;
+ gf u, q, tmp, num1, num2, den, discr_r;
+ gf recd[NN];
+ /* Err+Eras Locator poly and syndrome poly */
+ /*gf lambda[NN-KK + 1], s[NN-KK + 1];
+ gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
+ gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];*/
+ gf lambda[NN + 1], s[NN + 1];
+ gf b[NN + 1], t[NN + 1], omega[NN + 1];
+ gf root[NN], reg[NN + 1], loc[NN];
+ int syn_error, count;
+
+ /* data[] is in polynomial form, copy and convert to index form */
+ for (i = NN - 1; i >= 0; i--) {
#if (MM != 8)
- if(data[i] > NN)
- return -1; /* Illegal symbol */
+ if (data[i] > NN) {
+ return -1; /* Illegal symbol */
+ }
#endif
- recd[i] = Index_of[data[i]];
- }
- /* first form the syndromes; i.e., evaluate recd(x) at roots of g(x)
- * namely @**(B0+i), i = 0, ... ,(NN-KK-1)
- */
- syn_error = 0;
- for (i = 1; i <= NN-KK; i++) {
- tmp = 0;
- for (j = 0; j < NN; j++)
- if (recd[j] != A0) /* recd[j] in index form */
- tmp ^= Alpha_to[modnn(recd[j] + (B0+i-1)*j)];
- syn_error |= tmp; /* set flag if non-zero syndrome =>
- * error */
- /* store syndrome in index form */
- s[i] = Index_of[tmp];
- }
- if (!syn_error) {
- /*
- * if syndrome is zero, data[] is a codeword and there are no
- * errors to correct. So return data[] unmodified
- */
- return 0;
- }
- CLEAR(&lambda[1],NN-KK);
- lambda[0] = 1;
- if (no_eras > 0) {
- /* Init lambda to be the erasure locator polynomial */
- lambda[1] = Alpha_to[eras_pos[0]];
- for (i = 1; i < no_eras; i++) {
- u = eras_pos[i];
- for (j = i+1; j > 0; j--) {
- tmp = Index_of[lambda[j - 1]];
- if(tmp != A0)
- lambda[j] ^= Alpha_to[modnn(u + tmp)];
- }
- }
+ recd[i] = Index_of[data[i]];
+ }
+ /* first form the syndromes; i.e., evaluate recd(x) at roots of g(x)
+ * namely @**(B0+i), i = 0, ... ,(NN-KK-1)
+ */
+ syn_error = 0;
+ for (i = 1; i <= NN - KK; i++) {
+ tmp = 0;
+ for (j = 0; j < NN; j++)
+ if (recd[j] != A0) { /* recd[j] in index form */
+ tmp ^= Alpha_to[modnn(recd[j] + (B0 + i - 1) * j)];
+ }
+ syn_error |= tmp; /* set flag if non-zero syndrome =>
+ * error */
+ /* store syndrome in index form */
+ s[i] = Index_of[tmp];
+ }
+ if (!syn_error) {
+ /*
+ * if syndrome is zero, data[] is a codeword and there are no
+ * errors to correct. So return data[] unmodified
+ */
+ return 0;
+ }
+ CLEAR(&lambda[1], NN - KK);
+ lambda[0] = 1;
+ if (no_eras > 0) {
+ /* Init lambda to be the erasure locator polynomial */
+ lambda[1] = Alpha_to[eras_pos[0]];
+ for (i = 1; i < no_eras; i++) {
+ u = eras_pos[i];
+ for (j = i + 1; j > 0; j--) {
+ tmp = Index_of[lambda[j - 1]];
+ if (tmp != A0) {
+ lambda[j] ^= Alpha_to[modnn(u + tmp)];
+ }
+ }
+ }
#ifdef ERASURE_DEBUG
- /* 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; i <= NN; i++) {
- 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) {
- /* store root and error location
- * number indices
- */
- root[count] = i;
- loc[count] = NN - i;
- count++;
- }
- }
- if (count != no_eras) {
- printf("\n lambda(x) is WRONG\n");
- return -1;
- }
+ /* 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; i <= NN; i++) {
+ 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) {
+ /* store root and error location
+ * number indices
+ */
+ root[count] = i;
+ loc[count] = NN - i;
+ count++;
+ }
+ }
+ if (count != no_eras) {
+ printf("\n lambda(x) is WRONG\n");
+ return -1;
+ }
#ifndef NO_PRINT
- 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");
+ 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; i <= NN; i++) {
- 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) {
- /* store root (index-form) and error location number */
- root[count] = i;
- loc[count] = NN - i;
- count++;
- }
- }
+ }
+ 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; i <= NN; i++) {
+ 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) {
+ /* store root (index-form) and error location number */
+ root[count] = i;
+ loc[count] = NN - i;
+ count++;
+ }
+ }
#ifdef DEBUG
- printf("\n Final error positions:\t");
- for (i = 0; i < count; i++)
- printf("%d ", loc[i]);
- printf("\n");
+ printf("\n Final error positions:\t");
+ for (i = 0; i < count; i++) {
+ printf("%d ", loc[i]);
+ }
+ printf("\n");
#endif
- if (deg_lambda != count) {
- /*
- * deg(lambda) unequal to number of roots => uncorrectable
- * error detected
- */
- return -1;
- }
- /*
- * 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 (deg_lambda != count) {
+ /*
+ * deg(lambda) unequal to number of roots => uncorrectable
+ * error detected
+ */
+ return -1;
+ }
+ /*
+ * 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) {
#ifdef DEBUG
- printf("\n ERROR: denominator = 0\n");
+ printf("\n ERROR: denominator = 0\n");
#endif
- return -1;
- }
- /* Apply error to data */
- if (num1 != 0) {
- data[loc[j]] ^= Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
- }
- }
- return count;
+ return -1;
+ }
+ /* Apply error to data */
+ if (num1 != 0) {
+ data[loc[j]] ^= Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN -
+ Index_of[den])];
+ }
+ }
+ return count;
}
projects / openjpeg.git / blobdiff