From 7fa30ea26aded931f45a5623ebb0752f24669e3c Mon Sep 17 00:00:00 2001 From: Stephen L Date: Sun, 5 Mar 2017 16:15:13 +0100 Subject: [PATCH] Error correction for network packets, proof of concept (untested) Signed-off-by: Stephen L. --- code/qcommon/msg.c | 45 +++ code/qcommon/net_chan.c | 23 +- code/rscode/LICENSE | 10 + code/rscode/Makefile | 50 +++ code/rscode/README | 27 ++ code/rscode/berlekamp.c | 324 +++++++++++++++++++ code/rscode/config.doc | 18 ++ code/rscode/crcgen.c | 66 ++++ code/rscode/ecc.h | 100 ++++++ code/rscode/example.c | 128 ++++++++ code/rscode/galois.c | 112 +++++++ code/rscode/gpl.txt | 674 ++++++++++++++++++++++++++++++++++++++++ code/rscode/rs.c | 201 ++++++++++++ code/rscode/rs.doc | 86 +++++ 14 files changed, 1863 insertions(+), 1 deletion(-) create mode 100644 code/rscode/LICENSE create mode 100644 code/rscode/Makefile create mode 100644 code/rscode/README create mode 100644 code/rscode/berlekamp.c create mode 100644 code/rscode/config.doc create mode 100644 code/rscode/crcgen.c create mode 100644 code/rscode/ecc.h create mode 100644 code/rscode/example.c create mode 100644 code/rscode/galois.c create mode 100644 code/rscode/gpl.txt create mode 100644 code/rscode/rs.c create mode 100644 code/rscode/rs.doc diff --git a/code/qcommon/msg.c b/code/qcommon/msg.c index 20dec91d..2a0b0b21 100644 --- a/code/qcommon/msg.c +++ b/code/qcommon/msg.c @@ -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 (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) { diff --git a/code/qcommon/net_chan.c b/code/qcommon/net_chan.c index 0b099b95..20a1b54f 100644 --- a/code/qcommon/net_chan.c +++ b/code/qcommon/net_chan.c @@ -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 ); diff --git a/code/rscode/LICENSE b/code/rscode/LICENSE new file mode 100644 index 00000000..daab5a62 --- /dev/null +++ b/code/rscode/LICENSE @@ -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 + diff --git a/code/rscode/Makefile b/code/rscode/Makefile new file mode 100644 index 00000000..daa12624 --- /dev/null +++ b/code/rscode/Makefile @@ -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. + diff --git a/code/rscode/README b/code/rscode/README new file mode 100644 index 00000000..92d68b3d --- /dev/null +++ b/code/rscode/README @@ -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 + + diff --git a/code/rscode/berlekamp.c b/code/rscode/berlekamp.c new file mode 100644 index 00000000..dfe1b102 --- /dev/null +++ b/code/rscode/berlekamp.c @@ -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 . + * + * 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 +#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= 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); + } +} + diff --git a/code/rscode/config.doc b/code/rscode/config.doc new file mode 100644 index 00000000..77771893 --- /dev/null +++ b/code/rscode/config.doc @@ -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. + diff --git a/code/rscode/crcgen.c b/code/rscode/crcgen.c new file mode 100644 index 00000000..487dba5d --- /dev/null +++ b/code/rscode/crcgen.c @@ -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 . + + * 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); +} + diff --git a/code/rscode/ecc.h b/code/rscode/ecc.h new file mode 100644 index 00000000..1bfd457b --- /dev/null +++ b/code/rscode/ecc.h @@ -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 . + * + * 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[]); diff --git a/code/rscode/example.c b/code/rscode/example.c new file mode 100644 index 00000000..b4df5b87 --- /dev/null +++ b/code/rscode/example.c @@ -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 . + + * 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 +#include +#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); +} + diff --git a/code/rscode/galois.c b/code/rscode/galois.c new file mode 100644 index 00000000..57346c95 --- /dev/null +++ b/code/rscode/galois.c @@ -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 . + + * 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 +#include +#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]]); +} + diff --git a/code/rscode/gpl.txt b/code/rscode/gpl.txt new file mode 100644 index 00000000..94a9ed02 --- /dev/null +++ b/code/rscode/gpl.txt @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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But first, please read +. diff --git a/code/rscode/rs.c b/code/rscode/rs.c new file mode 100644 index 00000000..b8903076 --- /dev/null +++ b/code/rscode/rs.c @@ -0,0 +1,201 @@ +/* + * 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 . + + * Commercial licensing is available under a separate license, please + * contact author for details. + * + * Source code is available at http://rscode.sourceforge.net + */ + +#include +#include +#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); +} + diff --git a/code/rscode/rs.doc b/code/rscode/rs.doc new file mode 100644 index 00000000..651f76c7 --- /dev/null +++ b/code/rscode/rs.doc @@ -0,0 +1,86 @@ + + +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. + + +