diff --git a/plugins/h223/golay.c b/plugins/h223/golay.c new file mode 100644 index 0000000000..85eb540635 --- /dev/null +++ b/plugins/h223/golay.c @@ -0,0 +1,257 @@ +/* $Id$ + * + * 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. + * + * Ethereal - Network traffic analyzer + * By Gerald Combs + * 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., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + */ + +#include +#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<>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< 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<