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/*
* Provides routines for encoding and decoding the extended Golay
* (24,12,8) code.
*
* This implementation will detect up to 4 errors in a codeword (without
* being able to correct them); it will correct up to 3 errors.
*
* Wireshark  Network traffic analyzer
* By Gerald Combs <gerald@wireshark.org>
* Copyright 1998 Gerald Combs
*
* 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 2
* 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, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 021101301 USA.
*/
#include <glib.h>
#include "golay.h"
/* Encoding matrix, H
These entries are formed from the matrix specified in H.223/B.3.2.1.3;
it's first transposed so we have:
[P1 ] [111110010010] [MC1 ]
[P2 ] [011111001001] [MC2 ]
[P3 ] [110001110110] [MC3 ]
[P4 ] [011000111011] [MC4 ]
[P5 ] [110010001111] [MPL1]
[P6 ] = [100111010101] [MPL2]
[P7 ] [101101111000] [MPL3]
[P8 ] [010110111100] [MPL4]
[P9 ] [001011011110] [MPL5]
[P10] [000101101111] [MPL6]
[P11] [111100100101] [MPL7]
[P12] [101011100011] [MPL8]
So according to the equation, P1 = MC1+MC2+MC3+MC4+MPL1+MPL4+MPL7
Looking down the first column, we see that if MC1 is set, we toggle bits
1,3,5,6,7,11,12 of the parity: in binary, 110001110101 = 0xE3A
Similarly, to calculate the inverse, we read across the top of the table and
see that P1 is affected by bits MC1,MC2,MC3,MC4,MPL1,MPL4,MPL7: in binary,
111110010010 = 0x49F.
I've seen cunning implementations of this which only use one table. That
technique doesn't seem to work with these numbers though.
*/
static const guint golay_encode_matrix[12] = {
0xC75,
0x49F,
0xD4B,
0x6E3,
0x9B3,
0xB66,
0xECC,
0x1ED,
0x3DA,
0x7B4,
0xB1D,
0xE3A,
};
static const guint golay_decode_matrix[12] = {
0x49F,
0x93E,
0x6E3,
0xDC6,
0xF13,
0xAB9,
0x1ED,
0x3DA,
0x7B4,
0xF68,
0xA4F,
0xC75,
};
/* Function to compute the Hamming weight of a 12bit integer */
static guint weight12(guint vector)
{
guint w=0;
guint i;
for( i=0; i<12; i++ )
if( vector & 1<<i )
w++;
return w;
}
/* returns the golay coding of the given 12bit word */
static guint golay_coding(guint w)
{
guint out=0;
guint i;
for( i = 0; i<12; i++ ) {
if( w & 1<<i )
out ^= golay_encode_matrix[i];
}
return out;
}
/* encodes a 12bit word to a 24bit codeword */
guint32 golay_encode(guint w)
{
return ((guint32)w)  ((guint32)golay_coding(w))<<12;
}
/* returns the golay coding of the given 12bit word */
static guint golay_decoding(guint w)
{
guint out=0;
guint i;
for( i = 0; i<12; i++ ) {
if( w & 1<<(i) )
out ^= golay_decode_matrix[i];
}
return out;
}
/* return a mask showing the bits which are in error in a received
* 24bit codeword, or 1 if 4 errors were detected.
*/
gint32 golay_errors(guint32 codeword)
{
guint received_data, received_parity;
guint syndrome;
guint w,i;
guint inv_syndrome = 0;
received_parity = (guint)(codeword>>12);
received_data = (guint)codeword & 0xfff;
/* We use the C notation ^ for XOR to represent addition modulo 2.
*
* Model the received codeword (r) as the transmitted codeword (u)
* plus an error vector (e).
*
* r = e ^ u
*
* Then we calculate a syndrome (s):
*
* s = r * H, where H = [ P ], where I12 is the identity matrix
* [ I12 ]
*
* (In other words, we calculate the parity check for the received
* data bits, and add them to the received parity bits)
*/
syndrome = received_parity ^ (golay_coding(received_data));
w = weight12(syndrome);
/*
* The properties of the golay code are such that the Hamming distance (ie,
* the minimum distance between codewords) is 8; that means that one bit of
* error in the data bits will cause 7 errors in the parity bits.
*
* In particular, if we find 3 or fewer errors in the parity bits, either:
*  there are no errors in the data bits, or
*  there are at least 5 errors in the data bits
* we hope for the former (we don't profess to deal with the
* latter).
*/
if( w <= 3 ) {
return ((gint32) syndrome)<<12;
}
/* the next thing to try is one error in the data bits.
* we try each bit in turn and see if an error in that bit would have given
* us anything like the parity bits we got. At this point, we tolerate two
* errors in the parity bits, but three or more errors would give a total
* error weight of 4 or more, which means it's actually uncorrectable or
* closer to another codeword. */
for( i = 0; i<12; i++ ) {
guint error = 1<<i;
guint coding_error = golay_encode_matrix[i];
if( weight12(syndrome^coding_error) <= 2 ) {
return (gint32)((((guint32)(syndrome^coding_error))<<12)  (guint32)error) ;
}
}
/* okay then, let's see whether the parity bits are error free, and all the
* errors are in the data bits. model this as follows:
*
* [r  pr] = [u  pu] + [e  0]
*
* pr = pu
* pu = H * u => u = H' * pu = H' * pr , where H' is inverse of H
*
* we already have s = H*r + pr, so pr = s  H*r = s ^ H*r
* e = u ^ r
* = (H' * ( s ^ H*r )) ^ r
* = H'*s ^ r ^ r
* = H'*s
*
* Once again, we accept up to three error bits...
*/
inv_syndrome = golay_decoding(syndrome);
w = weight12(inv_syndrome);
if( w <=3 ) {
return (gint32)inv_syndrome;
}
/* Final shot: try with 2 errors in the data bits, and 1 in the parity
* bits; as before we try each of the bits in the parity in turn */
for( i = 0; i<12; i++ ) {
guint error = 1<<i;
guint coding_error = golay_decode_matrix[i];
if( weight12(inv_syndrome^coding_error) <= 2 ) {
guint32 error_word = ((guint32)(inv_syndrome^coding_error))  ((guint32)error)<<12;
return (gint32)error_word;
}
}
/* uncorrectable error */
return 1;
}
/* decode a received codeword. Up to 3 errors are corrected for; 4
errors are detected as uncorrectable (return 1); 5 or more errors
cause an incorrect correction.
*/
gint golay_decode(guint32 w)
{
guint data = (guint)w & 0xfff;
gint32 errors = golay_errors(w);
guint data_errors;
if( errors == 1 )
return 1;
data_errors = (guint)errors & 0xfff;
return (gint)(data ^ data_errors);
}
/*
* Editor modelines
*
* Local Variables:
* cbasicoffset: 4
* tabwidth: 8
* indenttabsmode: nil
* End:
*
* ex: set shiftwidth=4 tabstop=8 expandtab:
* :indentSize=4:tabSize=8:noTabs=true:
*/
