-
Notifications
You must be signed in to change notification settings - Fork 7
/
decode.c
280 lines (251 loc) · 9.12 KB
/
decode.c
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
#include <stdbool.h>
#include <stdio.h>
#include <string.h>
#include "Headers/array.h"
#include "Headers/op.h"
/*Given the received codeword msg and the number of error correcting symbols (nsym), computes the
syndromes polynomial. Mathematically, it's essentially equivalent to a Fourrier Transform
(Chien search being the inverse).*/
struct Array* rs_calc_syndromes(struct Array *msg, uint8_t nsym, struct gf_tables *gf_table)
{
struct Array *synd = malloc(sizeof(struct Array));
struct Array *res = malloc(sizeof(struct Array));
initZArray(synd, nsym+1);
initZArray(res, nsym+2);
for(uint8_t i = 0; i < nsym; i++){
synd->array[i] = gf_poly_eval(msg, gf_pow(2, i, gf_table), gf_table);
insertArray(synd);
}
insertArray(res);
for(uint8_t i = 1; i < nsym + 1; i++){
res->array[i] = synd->array[i-1]; //pad with one 0 for mathematical precision
insertArray(res);
}
//(else we can end up with weird calculations sometimes)
freeArray(synd);
return res;
}
/*Returns true if the message + ecc has no error of false otherwise (may not always catch a wrong
decoding or a wrong message,particularly if there are too many errors, but it usually does)*/
bool rs_check(struct Array *msg, uint8_t nsym, struct gf_tables *gf_table)
{
struct Array *synd = malloc(sizeof(struct Array));
initArray(synd, nsym+1);
synd = rs_calc_syndromes(msg, nsym, gf_table);
bool res = true;
for(uint8_t i = 0; i < nsym+1; i++)
res &= synd->array[i] == 0;
freeArray(synd);
return res;
}
struct Array* rs_find_errdata_locator(struct Array *e_pos, struct gf_tables *gf_table)
{
struct Array *e_loc = malloc(sizeof(struct Array));
initZArray(e_loc, e_pos->used+1);
e_loc->array[0] = 1;
insertArray(e_loc);
struct Array *one = malloc(sizeof(struct Array));
initZArray(one, 2);
one->array[0] = 1;
insertArray(one);
for(size_t i = 0; i < e_pos->used; i++){
uint8_t pow_two = gf_pow(2, e_pos->array[i], gf_table);
struct Array *arr = malloc(sizeof(struct Array));
initArray(arr, 2);
arr->array[0] = pow_two;
insertArray(arr);
arr->array[1] = 0;
insertArray(arr);
struct Array *add = gf_poly_add(one, arr);
e_loc = gf_poly_mul(e_loc, add, gf_table);
freeArray(arr);
}
freeArray(one);
return e_loc;
}
/*Compute the error (or erasures if you supply sigma=erasures locator polynomial, or errata) evaluator
polynomial Omega from the syndrome and the error/erasures/errata locator Sigma*/
struct Array* rs_find_error_evaluator(struct Array *synd, struct Array *err_loc, uint8_t nsym, struct gf_tables *gf_table)
{
struct Array *res = malloc(sizeof(struct Array));
initArray(res, nsym+2);
res = gf_poly_mul(synd, err_loc, gf_table);
size_t len = res->used - (nsym+1);
memmove(res->array, res->array+len, len);
res->used = res->used - len;
return res;
}
/*Forney algorithm, computes the values (error magnitude) to correct the input message.*/
struct Array* rs_correct_errdata(struct Array *msg_in, struct Array *synd, struct Array *err_pos, struct gf_tables *gf_table)
{
size_t len = msg_in->size;
struct Array *coef_pos = malloc(sizeof(struct Array));
struct Array *err_loc = malloc(sizeof(struct Array));
struct Array *rev_synd = reverse_arr(synd);
struct Array *err_eval = malloc(sizeof(struct Array));
struct Array *X = malloc(sizeof(struct Array));
struct Array *E = malloc(sizeof(struct Array));
initArray(coef_pos, err_pos->used+1);
for(size_t i = 0; i < err_pos->used; i++){
coef_pos->array[i] = len - 1 - err_pos->array[i];
insertArray(coef_pos);
}
initZArray(E, len);
initArray(err_loc, coef_pos->used+1);
err_loc= rs_find_errdata_locator(coef_pos, gf_table);
uint8_t nsym = err_loc->used - 1;
err_eval = rs_find_error_evaluator(rev_synd, err_loc, nsym, gf_table);
err_eval = reverse_arr(err_eval);
initArray(X, coef_pos->used);
for(size_t t = 0; t < coef_pos->used; t++){
uint8_t q = coef_pos->array[t];
X->array[t] = gf_pow(2, q, gf_table);
insertArray(X);
}
E->used = len;
for(size_t i = 0; i < X->used; i++){
struct Array *err_loc_prime_tmp = malloc(sizeof(struct Array));
uint8_t Xi_inv = gf_inverse(X->array[i], gf_table);
initArray(err_loc_prime_tmp, X->used+1);
for(size_t j = 0; j < X->used; j++){
if(j != i){
err_loc_prime_tmp->array[err_loc_prime_tmp->used] = gf_sub(1, gf_mul(Xi_inv, X->array[j], gf_table));
insertArray(err_loc_prime_tmp);
}
}
uint8_t err_loc_prime = 1;
for(size_t k = 0; k < err_loc_prime_tmp->used; k++)
err_loc_prime = gf_mul(err_loc_prime, err_loc_prime_tmp->array[k], gf_table);
uint8_t y = gf_poly_eval(reverse_arr(err_eval), Xi_inv, gf_table);
y = gf_mul(gf_pow(X->array[i], 1, gf_table), y, gf_table);
uint8_t magnitude = gf_div(y, err_loc_prime, gf_table);
E->array[err_pos->array[i]] = magnitude;
freeArray(err_loc_prime_tmp);
}
msg_in = gf_poly_add(msg_in, E);
freeArray(coef_pos);
freeArray(err_loc);
freeArray(rev_synd);
freeArray(err_eval);
return msg_in;
}
struct Array* rs_find_error_locator(struct Array* synd, uint8_t nsym, uint8_t erase_count, struct gf_tables *gf_table)
{
struct Array *err_loc = malloc(sizeof(struct Array*));
initZArray(err_loc, 10);
struct Array *old_loc = malloc(sizeof(struct Array*));
initZArray(old_loc, 10);
err_loc->array[0] = 1;
insertArray(err_loc);
old_loc->array[0] = 1;
insertArray(old_loc);
size_t synd_shift = 0;
if(synd->used > nsym)
synd_shift = synd->used - nsym;
for(int i = 0; i < nsym-erase_count;i++){
size_t K = i + synd_shift;
uint8_t delta = synd->array[K];
for(size_t j = 1 ; j < err_loc->used; j++){
delta ^= gf_mul(err_loc->array[err_loc->used - (j+1)], synd->array[K - j], gf_table);
}
old_loc->array[old_loc->used + 1] = 0;
insertArray(old_loc);
if(delta != 0){
if(old_loc->used > err_loc->used){
struct Array *new_loc = malloc(sizeof(struct Array*));
new_loc = gf_poly_scale(old_loc, delta, gf_table);
old_loc = gf_poly_scale(err_loc, gf_inverse(delta, gf_table), gf_table);
memmove(err_loc->array, new_loc->array, err_loc->used);
err_loc->used = new_loc->used;
}
struct Array *scale = malloc(sizeof(struct Array*));
scale = gf_poly_scale(old_loc, delta, gf_table);
err_loc = gf_poly_add(err_loc, scale);
}
}
while(err_loc->used && err_loc->array[0] == 0)
err_loc = pop_arr(err_loc);
size_t errs = err_loc->used - 1;
if(errs-erase_count * 2 + erase_count > nsym){
fprintf(stderr, "Too many errors to correct");
exit(EXIT_FAILURE);
}
freeArray(old_loc);
return err_loc;
}
struct Array* rs_find_errors(struct Array *err_loc, size_t nmess, struct gf_tables *gf_table)//nmess is len(msg_in)
{
size_t errs = err_loc->used - 1;
size_t counter = 0;
struct Array *err_pos = malloc(sizeof(struct Array*));
initArray(err_pos, errs);
for(size_t i = 0; i < nmess; i++){
if(gf_poly_eval(err_loc, gf_pow(2, i, gf_table), gf_table) == 0){
err_pos->array[counter] = nmess - 1 - i;
insertArray(err_pos);
counter++;
}
}
if(err_pos->used != errs){
fprintf(stderr, "Too many (or few) errors found by Chien Search for the errdata locator polynomial!");
exit(EXIT_FAILURE);
}
return err_pos;
}
struct Array* rs_forney_syndromes(struct Array *synd, struct Array *pos, uint8_t nmess, struct gf_tables *gf_table){
struct Array *erase_pos_reversed = malloc(sizeof(struct Array*));
initArray(erase_pos_reversed, pos->used);
for (size_t i = 0; i < pos->used; i++) {
erase_pos_reversed->array[i] = nmess - 1 - pos->array[i];
}
erase_pos_reversed->used = pos->used;
struct Array *fsynd = malloc(sizeof(struct Array*));
initArray(fsynd, synd->used);
memmove(fsynd->array, synd->array + 1, synd->used-1);
fsynd->used = synd->used - 1;
for (size_t i = 0; i < pos->used; i++) {
uint8_t x = gf_pow(2, erase_pos_reversed->array[i], gf_table);
for (size_t j = 0; j < fsynd->used - 1; j++)
fsynd->array[j] = gf_mul(fsynd->array[j], x, gf_table) ^ fsynd->array[j + 1];
}
freeArray(erase_pos_reversed);
return fsynd;
}
struct Array* rs_correct_msg(struct Array *msg_in, uint8_t nsym, struct Array *erase_pos, struct gf_tables *gf_table){
if (msg_in->used > 255) {
fprintf(stderr, "Message is too long ");
exit(EXIT_FAILURE);
}
struct Array *msg_out = malloc(sizeof(struct Array*));
initArray(msg_out, msg_in->used);
memmove(msg_out->array, msg_in->array, msg_in->used);
struct Array *synd = rs_calc_syndromes(msg_in, nsym, gf_table);
uint8_t max = synd->array[0];
for (size_t i = 0; i < synd->used; i++) {
max = synd->array[i] > max ? synd->array[i] : max;
}
if (max == 0) { //No errors
return msg_out;
}
//struct Array *fsynd = rs_forney_syndromes(synd, erase_pos, msg_out->used, gf_table);
struct Array *err_loc = rs_find_error_locator(synd, nsym, 0, gf_table);
struct Array *err_pos = rs_find_errors(reverse_arr(err_loc) , msg_in->used, gf_table);
if (err_pos == NULL) {
fprintf(stderr, "Could not locate error");
exit(EXIT_FAILURE);
}
msg_out = rs_correct_errdata(msg_in, synd, err_pos, gf_table);
synd = rs_calc_syndromes(msg_out, nsym, gf_table);
max = synd->array[0];
for (size_t i = 0; i < synd->used; i++) {
max = synd->array[i] > max ? synd->array[i] : max;
}
if (max > 0) { //Couldn't correct
fprintf(stderr, "Could not correct message");
exit(EXIT_FAILURE);
}
freeArray(synd);
freeArray(err_loc);
freeArray(err_pos);
return msg_out;
}