1 /* Reed-Solomon decoder
2 * Copyright 2002 Phil Karn, KA9Q
3 * May be used under the terms of the GNU Lesser General Public License (LGPL)
4 */
5
6 #ifdef DEBUG
7 #include <stdio.h>
8 #endif
9
10 #include <string.h>
11
12 #define NULL ((void *)0)
13 #define min(a,b) ((a) < (b) ? (a) : (b))
14
15 #ifdef FIXED
16 #include "fixed.h"
17 #elif defined(BIGSYM)
18 #include "int.h"
19 #else
20 #include "char.h"
21 #endif
22
DECODE_RS(data_t * data,int * eras_pos,int no_eras,int pad)23 int DECODE_RS(
24 #ifdef FIXED
25 data_t *data, int *eras_pos, int no_eras,int pad){
26 #else
27 void *p,data_t *data, int *eras_pos, int no_eras){
28 struct rs *rs = (struct rs *)p;
29 #endif
30 int deg_lambda, el, deg_omega;
31 int i, j, r,k;
32 data_t u,q,tmp,num1,num2,den,discr_r;
33 data_t lambda[NROOTS+1], s[NROOTS]; /* Err+Eras Locator poly
34 * and syndrome poly */
35 data_t b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1];
36 data_t root[NROOTS], reg[NROOTS+1], loc[NROOTS];
37 int syn_error, count;
38
39 #ifdef FIXED
40 /* Check pad parameter for validity */
41 if(pad < 0 || pad >= NN)
42 return -1;
43 #endif
44
45 /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
46 for(i=0;i<NROOTS;i++)
47 s[i] = data[0];
48
49 for(j=1;j<NN-PAD;j++){
50 for(i=0;i<NROOTS;i++){
51 if(s[i] == 0){
52 s[i] = data[j];
53 } else {
54 s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR+i)*PRIM)];
55 }
56 }
57 }
58
59 /* Convert syndromes to index form, checking for nonzero condition */
60 syn_error = 0;
61 for(i=0;i<NROOTS;i++){
62 syn_error |= s[i];
63 s[i] = INDEX_OF[s[i]];
64 }
65
66 if (!syn_error) {
67 /* if syndrome is zero, data[] is a codeword and there are no
68 * errors to correct. So return data[] unmodified
69 */
70 count = 0;
71 goto finish;
72 }
73 memset(&lambda[1],0,NROOTS*sizeof(lambda[0]));
74 lambda[0] = 1;
75
76 if (no_eras > 0) {
77 /* Init lambda to be the erasure locator polynomial */
78 lambda[1] = ALPHA_TO[MODNN(PRIM*(NN-1-eras_pos[0]))];
79 for (i = 1; i < no_eras; i++) {
80 u = MODNN(PRIM*(NN-1-eras_pos[i]));
81 for (j = i+1; j > 0; j--) {
82 tmp = INDEX_OF[lambda[j - 1]];
83 if(tmp != A0)
84 lambda[j] ^= ALPHA_TO[MODNN(u + tmp)];
85 }
86 }
87
88 #if DEBUG >= 1
89 /* Test code that verifies the erasure locator polynomial just constructed
90 Needed only for decoder debugging. */
91
92 /* find roots of the erasure location polynomial */
93 for(i=1;i<=no_eras;i++)
94 reg[i] = INDEX_OF[lambda[i]];
95
96 count = 0;
97 for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
98 q = 1;
99 for (j = 1; j <= no_eras; j++)
100 if (reg[j] != A0) {
101 reg[j] = MODNN(reg[j] + j);
102 q ^= ALPHA_TO[reg[j]];
103 }
104 if (q != 0)
105 continue;
106 /* store root and error location number indices */
107 root[count] = i;
108 loc[count] = k;
109 count++;
110 }
111 if (count != no_eras) {
112 printf("count = %d no_eras = %d\n lambda(x) is WRONG\n",count,no_eras);
113 count = -1;
114 goto finish;
115 }
116 #if DEBUG >= 2
117 printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
118 for (i = 0; i < count; i++)
119 printf("%d ", loc[i]);
120 printf("\n");
121 #endif
122 #endif
123 }
124 for(i=0;i<NROOTS+1;i++)
125 b[i] = INDEX_OF[lambda[i]];
126
127 /*
128 * Begin Berlekamp-Massey algorithm to determine error+erasure
129 * locator polynomial
130 */
131 r = no_eras;
132 el = no_eras;
133 while (++r <= NROOTS) { /* r is the step number */
134 /* Compute discrepancy at the r-th step in poly-form */
135 discr_r = 0;
136 for (i = 0; i < r; i++){
137 if ((lambda[i] != 0) && (s[r-i-1] != A0)) {
138 discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r-i-1])];
139 }
140 }
141 discr_r = INDEX_OF[discr_r]; /* Index form */
142 if (discr_r == A0) {
143 /* 2 lines below: B(x) <-- x*B(x) */
144 memmove(&b[1],b,NROOTS*sizeof(b[0]));
145 b[0] = A0;
146 } else {
147 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
148 t[0] = lambda[0];
149 for (i = 0 ; i < NROOTS; i++) {
150 if(b[i] != A0)
151 t[i+1] = lambda[i+1] ^ ALPHA_TO[MODNN(discr_r + b[i])];
152 else
153 t[i+1] = lambda[i+1];
154 }
155 if (2 * el <= r + no_eras - 1) {
156 el = r + no_eras - el;
157 /*
158 * 2 lines below: B(x) <-- inv(discr_r) *
159 * lambda(x)
160 */
161 for (i = 0; i <= NROOTS; i++)
162 b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
163 } else {
164 /* 2 lines below: B(x) <-- x*B(x) */
165 memmove(&b[1],b,NROOTS*sizeof(b[0]));
166 b[0] = A0;
167 }
168 memcpy(lambda,t,(NROOTS+1)*sizeof(t[0]));
169 }
170 }
171
172 /* Convert lambda to index form and compute deg(lambda(x)) */
173 deg_lambda = 0;
174 for(i=0;i<NROOTS+1;i++){
175 lambda[i] = INDEX_OF[lambda[i]];
176 if(lambda[i] != A0)
177 deg_lambda = i;
178 }
179 /* Find roots of the error+erasure locator polynomial by Chien search */
180 memcpy(®[1],&lambda[1],NROOTS*sizeof(reg[0]));
181 count = 0; /* Number of roots of lambda(x) */
182 for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
183 q = 1; /* lambda[0] is always 0 */
184 for (j = deg_lambda; j > 0; j--){
185 if (reg[j] != A0) {
186 reg[j] = MODNN(reg[j] + j);
187 q ^= ALPHA_TO[reg[j]];
188 }
189 }
190 if (q != 0)
191 continue; /* Not a root */
192 /* store root (index-form) and error location number */
193 #if DEBUG>=2
194 printf("count %d root %d loc %d\n",count,i,k);
195 #endif
196 root[count] = i;
197 loc[count] = k;
198 /* If we've already found max possible roots,
199 * abort the search to save time
200 */
201 if(++count == deg_lambda)
202 break;
203 }
204 if (deg_lambda != count) {
205 /*
206 * deg(lambda) unequal to number of roots => uncorrectable
207 * error detected
208 */
209 count = -1;
210 goto finish;
211 }
212 /*
213 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
214 * x**NROOTS). in index form. Also find deg(omega).
215 */
216 deg_omega = deg_lambda-1;
217 for (i = 0; i <= deg_omega;i++){
218 tmp = 0;
219 for(j=i;j >= 0; j--){
220 if ((s[i - j] != A0) && (lambda[j] != A0))
221 tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
222 }
223 omega[i] = INDEX_OF[tmp];
224 }
225
226 /*
227 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
228 * inv(X(l))**(FCR-1) and den = lambda_pr(inv(X(l))) all in poly-form
229 */
230 for (j = count-1; j >=0; j--) {
231 num1 = 0;
232 for (i = deg_omega; i >= 0; i--) {
233 if (omega[i] != A0)
234 num1 ^= ALPHA_TO[MODNN(omega[i] + i * root[j])];
235 }
236 num2 = ALPHA_TO[MODNN(root[j] * (FCR - 1) + NN)];
237 den = 0;
238
239 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
240 for (i = min(deg_lambda,NROOTS-1) & ~1; i >= 0; i -=2) {
241 if(lambda[i+1] != A0)
242 den ^= ALPHA_TO[MODNN(lambda[i+1] + i * root[j])];
243 }
244 #if DEBUG >= 1
245 if (den == 0) {
246 printf("\n ERROR: denominator = 0\n");
247 count = -1;
248 goto finish;
249 }
250 #endif
251 /* Apply error to data */
252 if (num1 != 0 && loc[j] >= PAD) {
253 data[loc[j]-PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])];
254 }
255 }
256 finish:
257 if(eras_pos != NULL){
258 for(i=0;i<count;i++)
259 eras_pos[i] = loc[i];
260 }
261 return count;
262 }
263