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wireshark/epan/reedsolomon.c

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/* reedsolomon.c
*
* Reed-Solomon encoding and decoding,
* by Phil Karn (karn@ka9q.ampr.org) September 1996
* Copyright 1999 Phil Karn, KA9Q
* Separate CCSDS version create Dec 1998, merged into this version May 1999
*
* This file is derived from my generic RS encoder/decoder, which is
* in turn based on 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
*
* Wireshark - Network traffic analyzer
* By Gerald Combs <gerald@wireshark.org>
* Copyright 1998 Gerald Combs
*
* SPDX-License-Identifier: GPL-2.0-or-later
*/
#include "config.h"
#define WS_LOG_DOMAIN LOG_DOMAIN_EPAN
#include <stdio.h>
#include "reedsolomon.h"
#include <wsutil/wslog.h>
#ifdef CCSDS
/* CCSDS field generator polynomial: 1+x+x^2+x^7+x^8 */
int Pp[MM+1] = { 1, 1, 1, 0, 0, 0, 0, 1, 1 };
#else /* not CCSDS */
/* MM, KK, B0, PRIM are user-defined in rs.h */
/* Primitive polynomials - see Lin & Costello, Appendix A,
* and Lee & Messerschmitt, p. 453.
*/
#if(MM == 2)/* Admittedly silly */
int Pp[MM+1] = { 1, 1, 1 };
#elif(MM == 3)
/* 1 + x + x^3 */
int Pp[MM+1] = { 1, 1, 0, 1 };
#elif(MM == 4)
/* 1 + x + x^4 */
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 };
#elif(MM == 6)
/* 1 + x + x^6 */
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 };
#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 };
#elif(MM == 9)
/* 1+x^4+x^9 */
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 };
#elif(MM == 11)
/* 1+x^2+x^11 */
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 };
#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 };
#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 };
#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 };
#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 };
#else
#error "Either CCSDS must be defined, or MM must be set in range 2-16"
#endif
#endif
#ifdef STANDARD_ORDER /* first byte transmitted is index of x**(KK-1) in message poly*/
/* definitions used in the encode routine*/
#define MESSAGE(i) data[KK-(i)-1]
#define REMAINDER(i) bb[NN-KK-(i)-1]
/* definitions used in the decode routine*/
#define RECEIVED(i) data[NN-1-(i)]
#define ERAS_INDEX(i) (NN-1-eras_pos[i])
#define INDEX_TO_POS(i) (NN-1-(i))
#else /* first byte transmitted is index of x**0 in message polynomial*/
/* definitions used in the encode routine*/
#define MESSAGE(i) data[i]
#define REMAINDER(i) bb[i]
/* definitions used in the decode routine*/
#define RECEIVED(i) data[i]
#define ERAS_INDEX(i) eras_pos[i]
#define INDEX_TO_POS(i) i
#endif
/* This defines the type used to store an element of the Galois Field
* used by the code. Make sure this is something larger than a char if
* if anything larger than GF(256) is used.
*
* Note: unsigned char will work up to GF(256) but int seems to run
* faster on the Pentium.
*/
typedef int gf;
/* index->polynomial form conversion table */
static gf Alpha_to[NN + 1];
/* Polynomial->index form conversion table */
static gf Index_of[NN + 1];
/* No legal value in index form represents zero, so
* we need a special value for this purpose
*/
#define A0 (NN)
/* Generator polynomial g(x) in index form */
static gf Gg[NN - KK + 1];
static int RS_init; /* Initialization flag */
/* Compute x % NN, where NN is 2**MM - 1,
* without a slow divide
*/
/* static inline gf*/
static gf
modnn(int 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];\
}
static void init_rs(void);
#ifdef CCSDS
/* Conversion lookup tables from conventional alpha to Berlekamp's
* dual-basis representation. Used in the CCSDS version only.
* taltab[] -- convert conventional to dual basis
* tal1tab[] -- convert dual basis to conventional
* Note: the actual RS encoder/decoder works with the conventional basis.
* So data is converted from dual to conventional basis before either
* encoding or decoding and then converted back.
*/
static unsigned char taltab[NN+1],tal1tab[NN+1];
static unsigned char tal[] = { 0x8d, 0xef, 0xec, 0x86, 0xfa, 0x99, 0xaf, 0x7b };
/* Generate conversion lookup tables between conventional alpha representation
* (@**7, @**6, ...@**0)
* and Berlekamp's dual basis representation
* (l0, l1, ...l7)
*/
static void
gen_ltab(void)
{
int i,j,k;
for(i=0;i<256;i++){/* For each value of input */
taltab[i] = 0;
for(j=0;j<8;j++) /* for each column of matrix */
for(k=0;k<8;k++){ /* for each row of matrix */
if(i & (1<<k))
taltab[i] ^= tal[7-k] & (1<<j);
}
tal1tab[taltab[i]] = i;
}
}
#endif /* CCSDS */
#if PRIM != 1
static int Ldec;/* Decrement for aux location variable in Chien search */
static void
gen_ldec(void)
{
for(Ldec=1;(Ldec % PRIM) != 0;Ldec+= NN)
;
Ldec /= PRIM;
}
#else
#define Ldec 1
#endif
/* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[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)
HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows:
Let @ represent the primitive element commonly called "alpha" that
is the root of the primitive polynomial p(x). Then in GF(2^m), for any
0 <= i <= 2^m-2,
@^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1)
where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation
of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for
example the polynomial representation of @^5 would be given by the binary
representation of the integer "alpha_to[5]".
Similarily, index_of[] can be used as follows:
As above, let @ represent the primitive element of GF(2^m) that is
the root of the primitive polynomial p(x). In order to find the power
of @ (alpha) that has the polynomial representation
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
representation is (a(0),a(1),a(2),...,a(m-1)).
NOTE:
The element alpha_to[2^m-1] = 0 always signifying that the
representation of "@^infinity" = 0 is (0,0,0,...,0).
Similarily, the element index_of[0] = A0 always signifying
that the power of alpha which has the polynomial representation
(0,0,...,0) is "infinity".
*/
static 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;
}
/*
* Obtain the generator polynomial of the TT-error correcting, length
* NN=(2**MM -1) Reed Solomon code from the product of (X+@**(B0+i)), i = 0,
* ... ,(2*TT-1)
*
* Examples:
*
* If B0 = 1, TT = 1. deg(g(x)) = 2*TT = 2.
* g(x) = (x+@) (x+@**2)
*
* If B0 = 0, TT = 2. deg(g(x)) = 2*TT = 4.
* g(x) = (x+1) (x+@) (x+@**2) (x+@**3)
*/
static void
gen_poly(void)
{
register int i, j;
Gg[0] = 1;
for (i = 0; i < NN - KK; i++) {
Gg[i+1] = 1;
/*
* Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
* (@**(B0+i)*PRIM + x)
*/
for (j = i; j > 0; j--)
if (Gg[j] != 0)
Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + (B0 + i) *PRIM)];
else
Gg[j] = Gg[j - 1];
/* Gg[0] can never be zero */
Gg[0] = Alpha_to[modnn(Index_of[Gg[0]] + (B0 + i) * PRIM)];
}
/* convert Gg[] to index form for quicker encoding */
for (i = 0; i <= NN - KK; i++)
Gg[i] = Index_of[Gg[i]];
}
/*
* take the string of symbols in data[i], i=0..(k-1) and encode
* systematically to produce NN-KK parity symbols in bb[0]..bb[NN-KK-1] data[]
* is input and bb[] is output in polynomial form. Encoding is done by using
* a feedback shift register with appropriate connections specified by the
* elements of Gg[], which was generated above. Codeword is c(X) =
* data(X)*X**(NN-KK)+ b(X)
*/
int
encode_rs(dtype data[], dtype bb[])
{
register int i, j;
gf feedback;
#if DEBUG >= 1 && MM != 8
/* Check for illegal input values */
for(i=0;i<KK;i++)
if(MESSAGE(i) > NN)
return -1;
#endif
if(!RS_init)
init_rs();
CLEAR(bb,NN-KK);
#ifdef CCSDS
/* Convert to conventional basis */
for(i=0;i<KK;i++)
MESSAGE(i) = tal1tab[MESSAGE(i)];
#endif
for(i = KK - 1; i >= 0; i--) {
feedback = Index_of[MESSAGE(i) ^ REMAINDER(NN - KK - 1)];
if (feedback != A0) { /* feedback term is non-zero */
for (j = NN - KK - 1; j > 0; j--)
if (Gg[j] != A0)
REMAINDER(j) = REMAINDER(j - 1) ^ Alpha_to[modnn(Gg[j] + feedback)];
else
REMAINDER(j) = REMAINDER(j - 1);
REMAINDER(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--)
REMAINDER(j) = REMAINDER(j - 1);
REMAINDER(0) = 0;
}
}
#ifdef CCSDS
/* Convert to l-basis */
for(i=0;i<NN;i++)
MESSAGE(i) = taltab[MESSAGE(i)];
#endif
return 0;
}
/*
* Performs ERRORS+ERASURES decoding of RS codes. If decoding is successful,
* writes the codeword into data[] itself. Otherwise data[] is unaltered.
*
* Return number of symbols corrected, or -1 if codeword is illegal
* or uncorrectable. If eras_pos is non-null, the detected error locations
* are written back. NOTE! This array must be at least NN-KK elements long.
*
* 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
* transmitted codeword will be recovered. Details of algorithm can be found
* in R. Blahut's "Theory ... of Error-Correcting Codes".
* Warning: the eras_pos[] array must not contain duplicate entries; decoder failure
* will result. The decoder *could* check for this condition, but it would involve
* extra time on every decoding operation.
*/
int
eras_dec_rs(dtype data[], int eras_pos[], int no_eras)
{
int deg_lambda, el, deg_omega;
int i, j, r,k;
gf u,q,tmp,num1,num2,den,discr_r;
gf lambda[NN-KK + 1], s[NN-KK + 1]; /* Err+Eras Locator poly
* and syndrome poly */
gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
gf root[NN-KK], reg[NN-KK + 1], loc[NN-KK];
int syn_error, count;
if(!RS_init)
init_rs();
#ifdef CCSDS
/* Convert to conventional basis */
for(i=0;i<NN;i++)
RECEIVED(i) = tal1tab[RECEIVED(i)];
#endif
#if DEBUG >= 1 && MM != 8
/* Check for illegal input values */
for(i=0;i<NN;i++)
if(RECEIVED(i) > NN)
return -1;
#endif
/* form the syndromes; i.e., evaluate data(x) at roots of g(x)
* namely @**(B0+i)*PRIM, i = 0, ... ,(NN-KK-1)
*/
for(i=1;i<=NN-KK;i++){
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];
/*ws_debug("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) {
ws_debug("\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(&reg[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
ws_debug("\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;
}
/*
* Editor modelines - https://www.wireshark.org/tools/modelines.html
*
* Local Variables:
* c-basic-offset: 2
* tab-width: 8
* indent-tabs-mode: nil
* End:
*
* ex: set shiftwidth=2 tabstop=8 expandtab:
* :indentSize=2:tabSize=8:noTabs=true:
*/
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