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Error correction for network packets, proof of concept (untested)

Browse source 
Signed-off-by: Stephen L. <lrq3000@gmail.com>
This commit is contained in:
Stephen L 2017-03-05 16:15:13 +01:00
parent 0374f0710b
commit 7fa30ea26a
14 changed files with 1863 additions and 1 deletions
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45
code/qcommon/msg.c
View file

@ -21,6 +21,7 @@ Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include "q_shared.h"
#include "qcommon.h"
#include "../rscode/ecc.h"
static huffman_t msgHuff;
@ -262,6 +263,31 @@ void MSG_WriteData( msg_t *buf, const void *data, int length ) {
}
}
void MSG_WriteDataWithECC( msg_t *buf, const void *data, int length ) {
int i;
char buf_copy[28];
char data_and_ecc[32];
for(i=0;i<length;i++) {
MSG_WriteByte(buf, ((byte *)data)[i]);
// copy the current byte in a buffer
buf_copy[i % 28] = ((byte *)data)[i];
// reached the size to generate an ecc, or we are at the end of the message
if i == 28 || i == (length - 1) {
// if end of message but the buffer is not full, we pad with 0s
if i == (length - 1) && (i % length) < 27 {
for(j=(i+1) % length;j<28;j++) {
buf_copy[j] = 0;
}
}
// generate ecc symbols (will be appended to the message)
encode_data(buf_copy, sizeof(buf_ecc), data_and_ecc);
for(j=28;j<sizeof(data_and_ecc);j++) {
MSG_WriteByte(buf, ((byte *)data_and_ecc)[i]);
}
}
}
}
void MSG_WriteShort( msg_t *sb, int c ) {
#ifdef PARANOID
if (c < ((short)0x8000) || c > (short)0x7fff)
@ -510,6 +536,25 @@ void MSG_ReadData( msg_t *msg, void *data, int len ) {
}
}
void MSG_ReadDataWithECC( msg_t *msg, void *data, int length ) {
int i;
char data_and_ecc[32];
// Decode each codeword blocks
for(i=0;i<(int)(length/32);i++) {
// Read codeword (data + ecc symbols)
MSG_ReadData(msg, data_and_ecc, 32);
// Decode the syndromes
decode_data(data_and_ecc, sizeof(data_and_ecc);
// Check the syndrome, if not null, then there are errors
if (check_syndrome () != 0) {
// Correct errors
correct_errors_erasures (data_and_ecc, sizeof(data_and_ecc), 0, 0); // disable erasures detection because we have no idea where the erasures might be, so just do error correction
// Copy the corrected message to data (ie, the first 28 bytes)
for(j=0;j<28;j++)
((byte *)data)[i*28+j] = data_and_ecc[j];
}
}
// a string hasher which gives the same hash value even if the
// string is later modified via the legacy MSG read/write code
int MSG_HashKey(const char *string, int maxlen) {

23
code/qcommon/net_chan.c
View file

@ -74,6 +74,7 @@ void Netchan_Init( int port ) {
showpackets = Cvar_Get ("showpackets", "0", CVAR_TEMP );
showdrop = Cvar_Get ("showdrop", "0", CVAR_TEMP );
qport = Cvar_Get ("net_qport", va("%i", port), CVAR_INIT );
initialize_ecc(); // initialize error correction lib
}
/*
@ -211,7 +212,9 @@ void Netchan_Transmit( netchan_t *chan, int length, const byte *data ) {
chan->outgoingSequence++;
MSG_WriteData( &send, data, length );
// Write data
//MSG_WriteData( &send, data, length );
MSG_WriteDataWithECC( &send, data, length );
// send the datagram
NET_SendPacket( chan->sock, send.cursize, send.data, chan->remoteAddress );
@ -245,6 +248,10 @@ qboolean Netchan_Process( netchan_t *chan, msg_t *msg ) {
int sequence;
int fragmentStart, fragmentLength;
qboolean fragmented;
// for error correction
msg_t corrected_msg;
int bak_readcount = 0;
int bak_bit = 0;
// XOR unscramble all data in the packet after the header
// Netchan_UnScramblePacket( msg );
@ -277,6 +284,20 @@ qboolean Netchan_Process( netchan_t *chan, msg_t *msg ) {
return qfalse;
}
// Apply error correction on message data if not fragmented (FIXME: implement also for fragmented packets)
if ( !fragmented ) {
// Store current cursor position
bak_readcount = msg->readcount;
bak_bit = msg->bit;
// Read and ecc decode message content
MSG_ReadDataWithECC( msg, corrected_msg, sizeof(msg));
// Replace current message with the corrected one, and restore cursor position
Q_strncpyz(msg, corrected_msg, MAX_PACKETLEN);
MSG_BeginReadingOOB( msg );
msg->readcount = bak_readcount;
msg->bit = bak_bit;
}
// read the fragment information
if ( fragmented ) {
fragmentStart = MSG_ReadShort( msg );

10
code/rscode/LICENSE Normal file
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@ -0,0 +1,10 @@
* (C) Henry Minsky (hqm@alum.mit.edu) 1991-2009
*
* This software library is licensed under terms of the GNU GENERAL
* PUBLIC LICENSE. [See file gpl.txt]
*
* Commercial licensing is available under a separate license, please
* contact author for details.
*
* Latest source code and other info at http://rscode.sourceforge.net

50
code/rscode/Makefile Normal file
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@ -0,0 +1,50 @@
# Makefile for Cross Interleaved Reed Solomon encoder/decoder
#
# (c) Henry Minsky, Universal Access 1991-1996
#
RANLIB = ranlib
AR = ar
VERSION = 1.0
DIRNAME= rscode-$(VERSION)
CC = gcc
# OPTIMIZE_FLAGS = -O69
DEBUG_FLAGS = -g
CFLAGS = -Wall -Wstrict-prototypes $(OPTIMIZE_FLAGS) $(DEBUG_FLAGS) -I..
LDFLAGS = $(OPTIMIZE_FLAGS) $(DEBUG_FLAGS)
LIB_CSRC = rs.c galois.c berlekamp.c crcgen.c
LIB_HSRC = ecc.h
LIB_OBJS = rs.o galois.o berlekamp.o crcgen.o
TARGET_LIB = libecc.a
TEST_PROGS = example
TARGETS = $(TARGET_LIB) $(TEST_PROGS)
all: $(TARGETS)
$(TARGET_LIB): $(LIB_OBJS)
$(RM) $@
$(AR) cq $@ $(LIB_OBJS)
if [ "$(RANLIB)" ]; then $(RANLIB) $@; fi
example: example.o galois.o berlekamp.o crcgen.o rs.o
gcc -o example example.o -L. -lecc
clean:
rm -f *.o example libecc.a
rm -f *~
dist:
(cd ..; tar -cvf rscode-$(VERSION).tar $(DIRNAME))
depend:
makedepend $(SRCS)
# DO NOT DELETE THIS LINE -- make depend depends on it.

27
code/rscode/README Normal file
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@ -0,0 +1,27 @@
RSCODE version 1.3
See the files
config.doc documentation of some compile time parameters
rs.doc overview of the Reed-Solomon coding program
rs.man a man page, slightly outdated at this point
example.c a simple example of encoding,decoding, and error correction
Makefile should work on a Sun system, may require GNU make.
Henry Minsky
hqm@alum.mit.edu
* (c) Henry Minsky (hqm@alum.mit.edu) 1991-2009
*
* This software library is licensed under terms of the GNU GENERAL
* PUBLIC LICENSE. (See gpl.txt)
*
* Commercial licensing is available under a separate license, please
* contact author for details.
*
* Source code is available at http://rscode.sourceforge.net

324
code/rscode/berlekamp.c Normal file
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@ -0,0 +1,324 @@
/***********************************************************************
* 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 < NPAR; 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 < NPAR; 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 < NPAR+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 <= NPAR) && 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);
}
}

18
code/rscode/config.doc Normal file
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@ -0,0 +1,18 @@
The basic coding parameters are defined using
macros, and an executable can be made by compiling using macro
definitions defining the values of the following names in the file
"ecc.h":
The important compile time parameter is the number of parity bytes,
specified by the #define NPAR.
The library is shipped with
#define NPAR 4
The error-correction routines are polynomial in the number of
parity bytes, so try to keep NPAR small for high performance.
Remember, the sum of the message length (in bytes) plus parity bytes
must be less than or equal to 255.

66
code/rscode/crcgen.c Normal file
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@ -0,0 +1,66 @@
/*****************************
* 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
*
* CRC-CCITT generator simulator for byte wide data.
*
*
* CRC-CCITT = x^16 + x^12 + x^5 + 1
*
*
******************************/
#include "ecc.h"
BIT16 crchware(BIT16 data, BIT16 genpoly, BIT16 accum);
/* Computes the CRC-CCITT checksum on array of byte data, length len
*/
BIT16 crc_ccitt(unsigned char *msg, int len)
{
int i;
BIT16 acc = 0;
for (i = 0; i < len; i++) {
acc = crchware((BIT16) msg[i], (BIT16) 0x1021, acc);
}
return(acc);
}
/* models crc hardware (minor variation on polynomial division algorithm) */
BIT16 crchware(BIT16 data, BIT16 genpoly, BIT16 accum)
{
static BIT16 i;
data <<= 8;
for (i = 8; i > 0; i--) {
if ((data ^ accum) & 0x8000)
accum = ((accum << 1) ^ genpoly) & 0xFFFF;
else
accum = (accum<<1) & 0xFFFF;
data = (data<<1) & 0xFFFF;
}
return (accum);
}

100
code/rscode/ecc.h Normal file
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@ -0,0 +1,100 @@
/* Reed Solomon Coding for glyphs
* 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/>.
*
* Source code is available at http://rscode.sourceforge.net
*
* Commercial licensing is available under a separate license, please
* contact author for details.
*
*/
/****************************************************************
Below is NPAR, the only compile-time parameter you should have to
modify.
It is the number of parity bytes which will be appended to
your data to create a codeword.
Note that the maximum codeword size is 255, so the
sum of your message length plus parity should be less than
or equal to this maximum limit.
In practice, you will get slooow error correction and decoding
if you use more than a reasonably small number of parity bytes.
(say, 10 or 20)
****************************************************************/
#define NPAR 4
/****************************************************************/
#define TRUE 1
#define FALSE 0
typedef unsigned long BIT32;
typedef unsigned short BIT16;
/* **************************************************************** */
/* Maximum degree of various polynomials. */
#define MAXDEG (NPAR*2)
/*************************************/
/* Encoder parity bytes */
extern int pBytes[MAXDEG];
/* Decoder syndrome bytes */
extern int synBytes[MAXDEG];
/* print debugging info */
extern int DEBUG;
/* Reed Solomon encode/decode routines */
void initialize_ecc (void);
int check_syndrome (void);
void decode_data (unsigned char data[], int nbytes);
void encode_data (unsigned char msg[], int nbytes, unsigned char dst[]);
/* CRC-CCITT checksum generator */
BIT16 crc_ccitt(unsigned char *msg, int len);
/* galois arithmetic tables */
extern int gexp[];
extern int glog[];
void init_galois_tables (void);
int ginv(int elt);
int gmult(int a, int b);
/* Error location routines */
int correct_errors_erasures (unsigned char codeword[], int csize,int nerasures, int erasures[]);
/* polynomial arithmetic */
void add_polys(int dst[], int src[]) ;
void scale_poly(int k, int poly[]);
void mult_polys(int dst[], int p1[], int p2[]);
void copy_poly(int dst[], int src[]);
void zero_poly(int poly[]);

128
code/rscode/example.c Normal file
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@ -0,0 +1,128 @@
/* Example use of Reed-Solomon library
*
* 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.
*
* This same code demonstrates the use of the encodier and
* decoder/error-correction routines.
*
* We are assuming we have at least four bytes of parity (NPAR >= 4).
*
* This gives us the ability to correct up to two errors, or
* four erasures.
*
* In general, with E errors, and K erasures, you will need
* 2E + K bytes of parity to be able to correct the codeword
* back to recover the original message data.
*
* You could say that each error 'consumes' two bytes of the parity,
* whereas each erasure 'consumes' one byte.
*
* Thus, as demonstrated below, we can inject one error (location unknown)
* and two erasures (with their locations specified) and the
* error-correction routine will be able to correct the codeword
* back to the original message.
* */
#include <stdio.h>
#include <stdlib.h>
#include "ecc.h"
unsigned char msg[] = "Nervously I loaded the twin ducks aboard the revolving pl\
atform.";
unsigned char codeword[256];
/* Some debugging routines to introduce errors or erasures
into a codeword.
*/
/* Introduce a byte error at LOC */
void
byte_err (int err, int loc, unsigned char *dst)
{
printf("Adding Error at loc %d, data %#x\n", loc, dst[loc-1]);
dst[loc-1] ^= err;
}
/* Pass in location of error (first byte position is
labeled starting at 1, not 0), and the codeword.
*/
void
byte_erasure (int loc, unsigned char dst[], int cwsize, int erasures[])
{
printf("Erasure at loc %d, data %#x\n", loc, dst[loc-1]);
dst[loc-1] = 0;
}
int
main (int argc, char *argv[])
{
int erasures[16];
int nerasures = 0;
/* Initialization the ECC library */
initialize_ecc ();
/* ************** */
/* Encode data into codeword, adding NPAR parity bytes */
encode_data(msg, sizeof(msg), codeword);
printf("Encoded data is: \"%s\"\n", codeword);
#define ML (sizeof (msg) + NPAR)
/* Add one error and two erasures */
byte_err(0x35, 3, codeword);
byte_err(0x23, 17, codeword);
byte_err(0x34, 19, codeword);
printf("with some errors: \"%s\"\n", codeword);
/* We need to indicate the position of the erasures. Eraseure
positions are indexed (1 based) from the end of the message... */
erasures[nerasures++] = ML-17;
erasures[nerasures++] = ML-19;
/* Now decode -- encoded codeword size must be passed */
decode_data(codeword, ML);
/* check if syndrome is all zeros */
if (check_syndrome () != 0) {
correct_errors_erasures (codeword,
ML,
nerasures,
erasures);
printf("Corrected codeword: \"%s\"\n", codeword);
}
exit(0);
}

112
code/rscode/galois.c Normal file
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@ -0,0 +1,112 @@
/*****************************
* 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
*
*
* Multiplication and Arithmetic on Galois Field GF(256)
*
* From Mee, Daniel, "Magnetic Recording, Volume III", Ch. 5 by Patel.
*
*
******************************/
#include <stdio.h>
#include <stdlib.h>
#include "ecc.h"
/* This is one of 14 irreducible polynomials
* of degree 8 and cycle length 255. (Ch 5, pp. 275, Magnetic Recording)
* The high order 1 bit is implicit */
/* x^8 + x^4 + x^3 + x^2 + 1 */
#define PPOLY 0x1D
int gexp[512];
int glog[256];
static void init_exp_table (void);
void
init_galois_tables (void)
{
/* initialize the table of powers of alpha */
init_exp_table();
}
static void
init_exp_table (void)
{
int i, z;
int pinit,p1,p2,p3,p4,p5,p6,p7,p8;
pinit = p2 = p3 = p4 = p5 = p6 = p7 = p8 = 0;
p1 = 1;
gexp[0] = 1;
gexp[255] = gexp[0];
glog[0] = 0; /* shouldn't log[0] be an error? */
for (i = 1; i < 256; i++) {
pinit = p8;
p8 = p7;
p7 = p6;
p6 = p5;
p5 = p4 ^ pinit;
p4 = p3 ^ pinit;
p3 = p2 ^ pinit;
p2 = p1;
p1 = pinit;
gexp[i] = p1 + p2*2 + p3*4 + p4*8 + p5*16 + p6*32 + p7*64 + p8*128;
gexp[i+255] = gexp[i];
}
for (i = 1; i < 256; i++) {
for (z = 0; z < 256; z++) {
if (gexp[z] == i) {
glog[i] = z;
break;
}
}
}
}
/* multiplication using logarithms */
int gmult(int a, int b)
{
int i,j;
if (a==0 || b == 0) return (0);
i = glog[a];
j = glog[b];
return (gexp[i+j]);
}
int ginv (int elt)
{
return (gexp[255-glog[elt]]);
}

674
code/rscode/gpl.txt Normal file
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WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.
17. Interpretation of Sections 15 and 16.
If the disclaimer of warranty and limitation of liability provided
above cannot be given local legal effect according to their terms,
reviewing courts shall apply local law that most closely approximates
an absolute waiver of all civil liability in connection with the
Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.
END OF TERMS AND CONDITIONS
How to Apply These Terms to Your New Programs
If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.
To do so, attach the following notices to the program. It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.
<one line to give the program's name and a brief idea of what it does.>
Copyright (C) <year> <name of author>
This program 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.
This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
Also add information on how to contact you by electronic and paper mail.
If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:
<program> Copyright (C) <year> <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<http://www.gnu.org/licenses/>.
The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<http://www.gnu.org/philosophy/why-not-lgpl.html>.

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/*
* Reed Solomon Encoder/Decoder
*
* 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
*/
#include <stdio.h>
#include <ctype.h>
#include "ecc.h"
/* Encoder parity bytes */
int pBytes[MAXDEG];
/* Decoder syndrome bytes */
int synBytes[MAXDEG];
/* generator polynomial */
int genPoly[MAXDEG*2];
int DEBUG = FALSE;
static void
compute_genpoly (int nbytes, int genpoly[]);
/* Initialize lookup tables, polynomials, etc. */
void
initialize_ecc ()
{
/* Initialize the galois field arithmetic tables */
init_galois_tables();
/* Compute the encoder generator polynomial */
compute_genpoly(NPAR, genPoly);
}
void
zero_fill_from (unsigned char buf[], int from, int to)
{
int i;
for (i = from; i < to; i++) buf[i] = 0;
}
/* debugging routines */
void
print_parity (void)
{
int i;
printf("Parity Bytes: ");
for (i = 0; i < NPAR; i++)
printf("[%d]:%x, ",i,pBytes[i]);
printf("\n");
}
void
print_syndrome (void)
{
int i;
printf("Syndrome Bytes: ");
for (i = 0; i < NPAR; i++)
printf("[%d]:%x, ",i,synBytes[i]);
printf("\n");
}
/* Append the parity bytes onto the end of the message */
void
build_codeword (unsigned char msg[], int nbytes, unsigned char dst[])
{
int i;
for (i = 0; i < nbytes; i++) dst[i] = msg[i];
for (i = 0; i < NPAR; i++) {
dst[i+nbytes] = pBytes[NPAR-1-i];
}
}
/**********************************************************
* Reed Solomon Decoder
*
* Computes the syndrome of a codeword. Puts the results
* into the synBytes[] array.
*/
void
decode_data(unsigned char data[], int nbytes)
{
int i, j, sum;
for (j = 0; j < NPAR; j++) {
sum = 0;
for (i = 0; i < nbytes; i++) {
sum = data[i] ^ gmult(gexp[j+1], sum);
}
synBytes[j] = sum;
}
}
/* Check if the syndrome is zero */
int
check_syndrome (void)
{
int i, nz = 0;
for (i =0 ; i < NPAR; i++) {
if (synBytes[i] != 0) {
nz = 1;
break;
}
}
return nz;
}
void
debug_check_syndrome (void)
{
int i;
for (i = 0; i < 3; i++) {
printf(" inv log S[%d]/S[%d] = %d\n", i, i+1,
glog[gmult(synBytes[i], ginv(synBytes[i+1]))]);
}
}
/* Create a generator polynomial for an n byte RS code.
* The coefficients are returned in the genPoly arg.
* Make sure that the genPoly array which is passed in is
* at least n+1 bytes long.
*/
static void
compute_genpoly (int nbytes, int genpoly[])
{
int i, tp[256], tp1[256];
/* multiply (x + a^n) for n = 1 to nbytes */
zero_poly(tp1);
tp1[0] = 1;
for (i = 1; i <= nbytes; i++) {
zero_poly(tp);
tp[0] = gexp[i]; /* set up x+a^n */
tp[1] = 1;
mult_polys(genpoly, tp, tp1);
copy_poly(tp1, genpoly);
}
}
/* Simulate a LFSR with generator polynomial for n byte RS code.
* Pass in a pointer to the data array, and amount of data.
*
* The parity bytes are deposited into pBytes[], and the whole message
* and parity are copied to dest to make a codeword.
*
*/
void
encode_data (unsigned char msg[], int nbytes, unsigned char dst[])
{
int i, LFSR[NPAR+1],dbyte, j;
for(i=0; i < NPAR+1; i++) LFSR[i]=0;
for (i = 0; i < nbytes; i++) {
dbyte = msg[i] ^ LFSR[NPAR-1];
for (j = NPAR-1; j > 0; j--) {
LFSR[j] = LFSR[j-1] ^ gmult(genPoly[j], dbyte);
}
LFSR[0] = gmult(genPoly[0], dbyte);
}
for (i = 0; i < NPAR; i++)
pBytes[i] = LFSR[i];
build_codeword(msg, nbytes, dst);
}

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Introduction to Reed Solomon Codes:
Henry Minsky, Universal Access Inc.
hqm@alum.mit.edu
[For details see Cain, Clark, "Error-Correction Coding For Digital
Communications", pp. 205.] The Reed-Solomon Code is an algebraic code
belonging to the class of BCH (Bose-Chaudry-Hocquehen) multiple burst
correcting cyclic codes. The Reed Solomon code operates on bytes of
fixed length.
Given m parity bytes, a Reed-Solomon code can correct up to m byte
errors in known positions (erasures), or detect and correct up to m/2
byte errors in unknown positions.
This is an implementation of a Reed-Solomon code with 8 bit bytes, and
a configurable number of parity bytes. The maximum sequence length
(codeword) that can be generated is 255 bytes, including parity bytes.
In practice, shorter sequences are used.
ENCODING: The basic principle of encoding is to find the remainder of
the message divided by a generator polynomial G(x). The encoder works
by simulating a Linear Feedback Shift Register with degree equal to
G(x), and feedback taps with the coefficents of the generating
polynomial of the code.
The rs.c file contains an algorithm to generate the encoder polynomial
for any number of bytes of parity, configurable as the NPAR constant
in the file ecc.h.
For this RS code, G(x) = (x-a^1)(x-a^2)(x-a^3)(x-a^4)...(x-a^NPAR)
where 'a' is a primitive element of the Galois Field GF(256) (== 2).
DECODING
The decoder generates four syndrome bytes, which will be all zero if
the message has no errors. If there are errors, the location and value
of the errors can be determined in a number of ways.
Computing the syndromes is easily done as a sum of products, see pp.
179 [Rhee 89].
Fundamentally, the syndome bytes form four simultaneous equations
which can be solved to find the error locations. Once error locations
are known, the syndrome bytes can be used to find the value of the
errors, and they can thus be corrected.
A simplified solution for locating and correcting single errors is
given in Cain and Clark, Ch. 5.
The more general error-location algorithm is the Berlekamp-Massey
algorithm, which will locate up to four errors, by iteratively solving
for the error-locator polynomial. The Modified Berlekamp Massey
algorithm takes as initial conditions any known suspicious bytes
(erasure flags) which you may have (such as might be flagged by
a laser demodulator, or deduced from a failure in a cross-interleaved
block code row or column).
Once the location of errors is known, error correction is done using
the error-evaluator polynomial.
APPLICATION IDEAS
As an example application, this library could be used to implement the
Compact Disc standard of 24 data bytes and 4 parity bytes. A RS code
with 24 data bytes and 4 parity bytes is referred to as a (28,24) RS
code. A (n, k) RS code is said to have efficiency k/n. This first
(28,24) coding is called the C2 or level 2 encoding, because in a
doubly encoded scheme, the codewords are decoded at the second
decoding step.
In following the approach used by Compact Disc digital audio, the 28
byte C2 codewords are four way interleaved and then the interleaved
data is encoded again with a (32,28) RS code. The is the C1 encoding
stage. This produces what is known as a "product code", and has
excellent error correction capability due to the imposition of
two-dimensional structure on the parity checks. The interleave helps
to insure against the case that a multibyte burst error wipes out more
than two bytes in each codeword. The cross-correction capability of
the product code can provide backup if in fact there are more than 2
uncorrectable errors in a block.