-
Notifications
You must be signed in to change notification settings - Fork 275
/
Hamming.cpp
349 lines (297 loc) · 10.5 KB
/
Hamming.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
/*
* Copyright (C) 2015,2016 by Jonathan Naylor G4KLX
*
* 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., 675 Mass Ave, Cambridge, MA 02139, USA.
*/
#include "Hamming.h"
#include <cstdio>
#include <cassert>
// Hamming (15,11,3) check a boolean data array
bool CHamming::decode15113_1(bool* d)
{
assert(d != NULL);
// Calculate the parity it should have
bool c0 = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[6];
bool c1 = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[7] ^ d[8] ^ d[9];
bool c2 = d[0] ^ d[1] ^ d[4] ^ d[5] ^ d[7] ^ d[8] ^ d[10];
bool c3 = d[0] ^ d[2] ^ d[4] ^ d[6] ^ d[7] ^ d[9] ^ d[10];
unsigned char n = 0U;
n |= (c0 != d[11]) ? 0x01U : 0x00U;
n |= (c1 != d[12]) ? 0x02U : 0x00U;
n |= (c2 != d[13]) ? 0x04U : 0x00U;
n |= (c3 != d[14]) ? 0x08U : 0x00U;
switch (n)
{
// Parity bit errors
case 0x01U: d[11] = !d[11]; return true;
case 0x02U: d[12] = !d[12]; return true;
case 0x04U: d[13] = !d[13]; return true;
case 0x08U: d[14] = !d[14]; return true;
// Data bit errors
case 0x0FU: d[0] = !d[0]; return true;
case 0x07U: d[1] = !d[1]; return true;
case 0x0BU: d[2] = !d[2]; return true;
case 0x03U: d[3] = !d[3]; return true;
case 0x0DU: d[4] = !d[4]; return true;
case 0x05U: d[5] = !d[5]; return true;
case 0x09U: d[6] = !d[6]; return true;
case 0x0EU: d[7] = !d[7]; return true;
case 0x06U: d[8] = !d[8]; return true;
case 0x0AU: d[9] = !d[9]; return true;
case 0x0CU: d[10] = !d[10]; return true;
// No bit errors
default: return false;
}
}
void CHamming::encode15113_1(bool* d)
{
assert(d != NULL);
// Calculate the checksum this row should have
d[11] = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[6];
d[12] = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[7] ^ d[8] ^ d[9];
d[13] = d[0] ^ d[1] ^ d[4] ^ d[5] ^ d[7] ^ d[8] ^ d[10];
d[14] = d[0] ^ d[2] ^ d[4] ^ d[6] ^ d[7] ^ d[9] ^ d[10];
}
// Hamming (15,11,3) check a boolean data array
bool CHamming::decode15113_2(bool* d)
{
assert(d != NULL);
// Calculate the checksum this row should have
bool c0 = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[5] ^ d[7] ^ d[8];
bool c1 = d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[6] ^ d[8] ^ d[9];
bool c2 = d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[7] ^ d[9] ^ d[10];
bool c3 = d[0] ^ d[1] ^ d[2] ^ d[4] ^ d[6] ^ d[7] ^ d[10];
unsigned char n = 0x00U;
n |= (c0 != d[11]) ? 0x01U : 0x00U;
n |= (c1 != d[12]) ? 0x02U : 0x00U;
n |= (c2 != d[13]) ? 0x04U : 0x00U;
n |= (c3 != d[14]) ? 0x08U : 0x00U;
switch (n) {
// Parity bit errors
case 0x01U: d[11] = !d[11]; return true;
case 0x02U: d[12] = !d[12]; return true;
case 0x04U: d[13] = !d[13]; return true;
case 0x08U: d[14] = !d[14]; return true;
// Data bit errors
case 0x09U: d[0] = !d[0]; return true;
case 0x0BU: d[1] = !d[1]; return true;
case 0x0FU: d[2] = !d[2]; return true;
case 0x07U: d[3] = !d[3]; return true;
case 0x0EU: d[4] = !d[4]; return true;
case 0x05U: d[5] = !d[5]; return true;
case 0x0AU: d[6] = !d[6]; return true;
case 0x0DU: d[7] = !d[7]; return true;
case 0x03U: d[8] = !d[8]; return true;
case 0x06U: d[9] = !d[9]; return true;
case 0x0CU: d[10] = !d[10]; return true;
// No bit errors
default: return false;
}
}
void CHamming::encode15113_2(bool* d)
{
assert(d != NULL);
// Calculate the checksum this row should have
d[11] = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[5] ^ d[7] ^ d[8];
d[12] = d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[6] ^ d[8] ^ d[9];
d[13] = d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[7] ^ d[9] ^ d[10];
d[14] = d[0] ^ d[1] ^ d[2] ^ d[4] ^ d[6] ^ d[7] ^ d[10];
}
// Hamming (13,9,3) check a boolean data array
bool CHamming::decode1393(bool* d)
{
assert(d != NULL);
// Calculate the checksum this column should have
bool c0 = d[0] ^ d[1] ^ d[3] ^ d[5] ^ d[6];
bool c1 = d[0] ^ d[1] ^ d[2] ^ d[4] ^ d[6] ^ d[7];
bool c2 = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[5] ^ d[7] ^ d[8];
bool c3 = d[0] ^ d[2] ^ d[4] ^ d[5] ^ d[8];
unsigned char n = 0x00U;
n |= (c0 != d[9]) ? 0x01U : 0x00U;
n |= (c1 != d[10]) ? 0x02U : 0x00U;
n |= (c2 != d[11]) ? 0x04U : 0x00U;
n |= (c3 != d[12]) ? 0x08U : 0x00U;
switch (n) {
// Parity bit errors
case 0x01U: d[9] = !d[9]; return true;
case 0x02U: d[10] = !d[10]; return true;
case 0x04U: d[11] = !d[11]; return true;
case 0x08U: d[12] = !d[12]; return true;
// Data bit erros
case 0x0FU: d[0] = !d[0]; return true;
case 0x07U: d[1] = !d[1]; return true;
case 0x0EU: d[2] = !d[2]; return true;
case 0x05U: d[3] = !d[3]; return true;
case 0x0AU: d[4] = !d[4]; return true;
case 0x0DU: d[5] = !d[5]; return true;
case 0x03U: d[6] = !d[6]; return true;
case 0x06U: d[7] = !d[7]; return true;
case 0x0CU: d[8] = !d[8]; return true;
// No bit errors
default: return false;
}
}
void CHamming::encode1393(bool* d)
{
assert(d != NULL);
// Calculate the checksum this column should have
d[9] = d[0] ^ d[1] ^ d[3] ^ d[5] ^ d[6];
d[10] = d[0] ^ d[1] ^ d[2] ^ d[4] ^ d[6] ^ d[7];
d[11] = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[5] ^ d[7] ^ d[8];
d[12] = d[0] ^ d[2] ^ d[4] ^ d[5] ^ d[8];
}
// Hamming (10,6,3) check a boolean data array
bool CHamming::decode1063(bool* d)
{
assert(d != NULL);
// Calculate the checksum this column should have
bool c0 = d[0] ^ d[1] ^ d[2] ^ d[5];
bool c1 = d[0] ^ d[1] ^ d[3] ^ d[5];
bool c2 = d[0] ^ d[2] ^ d[3] ^ d[4];
bool c3 = d[1] ^ d[2] ^ d[3] ^ d[4];
unsigned char n = 0x00U;
n |= (c0 != d[6]) ? 0x01U : 0x00U;
n |= (c1 != d[7]) ? 0x02U : 0x00U;
n |= (c2 != d[8]) ? 0x04U : 0x00U;
n |= (c3 != d[9]) ? 0x08U : 0x00U;
switch (n) {
// Parity bit errors
case 0x01U: d[6] = !d[6]; return true;
case 0x02U: d[7] = !d[7]; return true;
case 0x04U: d[8] = !d[8]; return true;
case 0x08U: d[9] = !d[9]; return true;
// Data bit erros
case 0x07U: d[0] = !d[0]; return true;
case 0x0BU: d[1] = !d[1]; return true;
case 0x0DU: d[2] = !d[2]; return true;
case 0x0EU: d[3] = !d[3]; return true;
case 0x0CU: d[4] = !d[4]; return true;
case 0x03U: d[5] = !d[5]; return true;
// No bit errors
default: return false;
}
}
void CHamming::encode1063(bool* d)
{
assert(d != NULL);
// Calculate the checksum this column should have
d[6] = d[0] ^ d[1] ^ d[2] ^ d[5];
d[7] = d[0] ^ d[1] ^ d[3] ^ d[5];
d[8] = d[0] ^ d[2] ^ d[3] ^ d[4];
d[9] = d[1] ^ d[2] ^ d[3] ^ d[4];
}
// A Hamming (16,11,4) Check
bool CHamming::decode16114(bool* d)
{
assert(d != NULL);
// Calculate the checksum this column should have
bool c0 = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[5] ^ d[7] ^ d[8];
bool c1 = d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[6] ^ d[8] ^ d[9];
bool c2 = d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[7] ^ d[9] ^ d[10];
bool c3 = d[0] ^ d[1] ^ d[2] ^ d[4] ^ d[6] ^ d[7] ^ d[10];
bool c4 = d[0] ^ d[2] ^ d[5] ^ d[6] ^ d[8] ^ d[9] ^ d[10];
// Compare these with the actual bits
unsigned char n = 0x00U;
n |= (c0 != d[11]) ? 0x01U : 0x00U;
n |= (c1 != d[12]) ? 0x02U : 0x00U;
n |= (c2 != d[13]) ? 0x04U : 0x00U;
n |= (c3 != d[14]) ? 0x08U : 0x00U;
n |= (c4 != d[15]) ? 0x10U : 0x00U;
switch (n) {
// Parity bit errors
case 0x01U: d[11] = !d[11]; return true;
case 0x02U: d[12] = !d[12]; return true;
case 0x04U: d[13] = !d[13]; return true;
case 0x08U: d[14] = !d[14]; return true;
case 0x10U: d[15] = !d[15]; return true;
// Data bit errors
case 0x19U: d[0] = !d[0]; return true;
case 0x0BU: d[1] = !d[1]; return true;
case 0x1FU: d[2] = !d[2]; return true;
case 0x07U: d[3] = !d[3]; return true;
case 0x0EU: d[4] = !d[4]; return true;
case 0x15U: d[5] = !d[5]; return true;
case 0x1AU: d[6] = !d[6]; return true;
case 0x0DU: d[7] = !d[7]; return true;
case 0x13U: d[8] = !d[8]; return true;
case 0x16U: d[9] = !d[9]; return true;
case 0x1CU: d[10] = !d[10]; return true;
// No bit errors
case 0x00U: return true;
// Unrecoverable errors
default: return false;
}
}
void CHamming::encode16114(bool* d)
{
assert(d != NULL);
d[11] = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[5] ^ d[7] ^ d[8];
d[12] = d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[6] ^ d[8] ^ d[9];
d[13] = d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[7] ^ d[9] ^ d[10];
d[14] = d[0] ^ d[1] ^ d[2] ^ d[4] ^ d[6] ^ d[7] ^ d[10];
d[15] = d[0] ^ d[2] ^ d[5] ^ d[6] ^ d[8] ^ d[9] ^ d[10];
}
// A Hamming (17,12,3) Check
bool CHamming::decode17123(bool* d)
{
assert(d != NULL);
// Calculate the checksum this column should have
bool c0 = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[6] ^ d[7] ^ d[9];
bool c1 = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[7] ^ d[8] ^ d[10];
bool c2 = d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[8] ^ d[9] ^ d[11];
bool c3 = d[0] ^ d[1] ^ d[4] ^ d[5] ^ d[7] ^ d[10];
bool c4 = d[0] ^ d[1] ^ d[2] ^ d[5] ^ d[6] ^ d[8] ^ d[11];
// Compare these with the actual bits
unsigned char n = 0x00U;
n |= (c0 != d[12]) ? 0x01U : 0x00U;
n |= (c1 != d[13]) ? 0x02U : 0x00U;
n |= (c2 != d[14]) ? 0x04U : 0x00U;
n |= (c3 != d[15]) ? 0x08U : 0x00U;
n |= (c4 != d[16]) ? 0x10U : 0x00U;
switch (n) {
// Parity bit errors
case 0x01U: d[12] = !d[12]; return true;
case 0x02U: d[13] = !d[13]; return true;
case 0x04U: d[14] = !d[14]; return true;
case 0x08U: d[15] = !d[15]; return true;
case 0x10U: d[16] = !d[16]; return true;
// Data bit errors
case 0x1BU: d[0] = !d[0]; return true;
case 0x1FU: d[1] = !d[1]; return true;
case 0x17U: d[2] = !d[2]; return true;
case 0x07U: d[3] = !d[3]; return true;
case 0x0EU: d[4] = !d[4]; return true;
case 0x1CU: d[5] = !d[5]; return true;
case 0x11U: d[6] = !d[6]; return true;
case 0x0BU: d[7] = !d[7]; return true;
case 0x16U: d[8] = !d[8]; return true;
case 0x05U: d[9] = !d[9]; return true;
case 0x0AU: d[10] = !d[10]; return true;
case 0x14U: d[11] = !d[11]; return true;
// No bit errors
case 0x00U: return true;
// Unrecoverable errors
default: return false;
}
}
void CHamming::encode17123(bool* d)
{
assert(d != NULL);
d[12] = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[6] ^ d[7] ^ d[9];
d[13] = d[0] ^ d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[7] ^ d[8] ^ d[10];
d[14] = d[1] ^ d[2] ^ d[3] ^ d[4] ^ d[5] ^ d[8] ^ d[9] ^ d[11];
d[15] = d[0] ^ d[1] ^ d[4] ^ d[5] ^ d[7] ^ d[10];
d[16] = d[0] ^ d[1] ^ d[2] ^ d[5] ^ d[6] ^ d[8] ^ d[11];
}