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

Signed-off-by: Stephen L. <lrq3000@gmail.com>

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<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) {

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 );

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
+

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.
+

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
+
+

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 <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);
+  }
+}
+

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. 
+

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 <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);
+}
+		

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 <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[]);

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 <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);
+}
+

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 <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]]);
+}
+

code/rscode/gpl.txt

@@ -0,0 +1,674 @@
+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
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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 <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);
+}
+

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.
+
+
+