258 lines
6.6 KiB
C
258 lines
6.6 KiB
C
/*
|
|
* 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
|
|
*
|
|
* SPDX-License-Identifier: GPL-2.0-or-later
|
|
*/
|
|
|
|
#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 12-bit 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 12-bit 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 12-bit word to a 24-bit codeword */
|
|
guint32 golay_encode(guint w)
|
|
{
|
|
return ((guint32)w) | ((guint32)golay_coding(w))<<12;
|
|
}
|
|
|
|
|
|
|
|
/* returns the golay coding of the given 12-bit 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
|
|
* 24-bit 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:
|
|
* c-basic-offset: 4
|
|
* tab-width: 8
|
|
* indent-tabs-mode: nil
|
|
* End:
|
|
*
|
|
* ex: set shiftwidth=4 tabstop=8 expandtab:
|
|
* :indentSize=4:tabSize=8:noTabs=true:
|
|
*/
|