blob: c165cf3de939adba4c02625c9c58c781e293d6ac [file] [log] [blame]
Bill Yi4e213d52015-06-23 13:53:11 -07001/* The guts of the Reed-Solomon decoder, meant to be #included
2 * into a function body with the following typedefs, macros and variables supplied
3 * according to the code parameters:
4
5 * data_t - a typedef for the data symbol
6 * data_t data[] - array of NN data and parity symbols to be corrected in place
7 * retval - an integer lvalue into which the decoder's return code is written
8 * NROOTS - the number of roots in the RS code generator polynomial,
9 * which is the same as the number of parity symbols in a block.
10 Integer variable or literal.
11 * NN - the total number of symbols in a RS block. Integer variable or literal.
12 * PAD - the number of pad symbols in a block. Integer variable or literal.
13 * ALPHA_TO - The address of an array of NN elements to convert Galois field
14 * elements in index (log) form to polynomial form. Read only.
15 * INDEX_OF - The address of an array of NN elements to convert Galois field
16 * elements in polynomial form to index (log) form. Read only.
17 * MODNN - a function to reduce its argument modulo NN. May be inline or a macro.
18 * FCR - An integer literal or variable specifying the first consecutive root of the
19 * Reed-Solomon generator polynomial. Integer variable or literal.
20 * PRIM - The primitive root of the generator poly. Integer variable or literal.
21 * DEBUG - If set to 1 or more, do various internal consistency checking. Leave this
22 * undefined for production code
23
24 * The memset(), memmove(), and memcpy() functions are used. The appropriate header
25 * file declaring these functions (usually <string.h>) must be included by the calling
26 * program.
27 */
28
29
30#if !defined(NROOTS)
31#error "NROOTS not defined"
32#endif
33
34#if !defined(NN)
35#error "NN not defined"
36#endif
37
38#if !defined(PAD)
39#error "PAD not defined"
40#endif
41
42#if !defined(ALPHA_TO)
43#error "ALPHA_TO not defined"
44#endif
45
46#if !defined(INDEX_OF)
47#error "INDEX_OF not defined"
48#endif
49
50#if !defined(MODNN)
51#error "MODNN not defined"
52#endif
53
54#if !defined(FCR)
55#error "FCR not defined"
56#endif
57
58#if !defined(PRIM)
59#error "PRIM not defined"
60#endif
61
62#if !defined(NULL)
63#define NULL ((void *)0)
64#endif
65
66#undef MIN
67#define MIN(a,b) ((a) < (b) ? (a) : (b))
68#undef A0
69#define A0 (NN)
70
71{
72 int deg_lambda, el, deg_omega;
73 int i, j, r,k;
74 data_t u,q,tmp,num1,num2,den,discr_r;
75 data_t lambda[NROOTS+1], s[NROOTS]; /* Err+Eras Locator poly
76 * and syndrome poly */
77 data_t b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1];
78 data_t root[NROOTS], reg[NROOTS+1], loc[NROOTS];
79 int syn_error, count;
80
81 /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
82 for(i=0;i<NROOTS;i++)
83 s[i] = data[0];
84
85 for(j=1;j<NN-PAD;j++){
86 for(i=0;i<NROOTS;i++){
87 if(s[i] == 0){
88 s[i] = data[j];
89 } else {
90 s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR+i)*PRIM)];
91 }
92 }
93 }
94
95 /* Convert syndromes to index form, checking for nonzero condition */
96 syn_error = 0;
97 for(i=0;i<NROOTS;i++){
98 syn_error |= s[i];
99 s[i] = INDEX_OF[s[i]];
100 }
101
102 if (!syn_error) {
103 /* if syndrome is zero, data[] is a codeword and there are no
104 * errors to correct. So return data[] unmodified
105 */
106 count = 0;
107 goto finish;
108 }
109 memset(&lambda[1],0,NROOTS*sizeof(lambda[0]));
110 lambda[0] = 1;
111
112 if (no_eras > 0) {
113 /* Init lambda to be the erasure locator polynomial */
114 lambda[1] = ALPHA_TO[MODNN(PRIM*(NN-1-eras_pos[0]))];
115 for (i = 1; i < no_eras; i++) {
116 u = MODNN(PRIM*(NN-1-eras_pos[i]));
117 for (j = i+1; j > 0; j--) {
118 tmp = INDEX_OF[lambda[j - 1]];
119 if(tmp != A0)
120 lambda[j] ^= ALPHA_TO[MODNN(u + tmp)];
121 }
122 }
123
124#if DEBUG >= 1
125 /* Test code that verifies the erasure locator polynomial just constructed
126 Needed only for decoder debugging. */
127
128 /* find roots of the erasure location polynomial */
129 for(i=1;i<=no_eras;i++)
130 reg[i] = INDEX_OF[lambda[i]];
131
132 count = 0;
133 for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
134 q = 1;
135 for (j = 1; j <= no_eras; j++)
136 if (reg[j] != A0) {
137 reg[j] = MODNN(reg[j] + j);
138 q ^= ALPHA_TO[reg[j]];
139 }
140 if (q != 0)
141 continue;
142 /* store root and error location number indices */
143 root[count] = i;
144 loc[count] = k;
145 count++;
146 }
147 if (count != no_eras) {
148 printf("count = %d no_eras = %d\n lambda(x) is WRONG\n",count,no_eras);
149 count = -1;
150 goto finish;
151 }
152#if DEBUG >= 2
153 printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
154 for (i = 0; i < count; i++)
155 printf("%d ", loc[i]);
156 printf("\n");
157#endif
158#endif
159 }
160 for(i=0;i<NROOTS+1;i++)
161 b[i] = INDEX_OF[lambda[i]];
162
163 /*
164 * Begin Berlekamp-Massey algorithm to determine error+erasure
165 * locator polynomial
166 */
167 r = no_eras;
168 el = no_eras;
169 while (++r <= NROOTS) { /* r is the step number */
170 /* Compute discrepancy at the r-th step in poly-form */
171 discr_r = 0;
172 for (i = 0; i < r; i++){
173 if ((lambda[i] != 0) && (s[r-i-1] != A0)) {
174 discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r-i-1])];
175 }
176 }
177 discr_r = INDEX_OF[discr_r]; /* Index form */
178 if (discr_r == A0) {
179 /* 2 lines below: B(x) <-- x*B(x) */
180 memmove(&b[1],b,NROOTS*sizeof(b[0]));
181 b[0] = A0;
182 } else {
183 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
184 t[0] = lambda[0];
185 for (i = 0 ; i < NROOTS; i++) {
186 if(b[i] != A0)
187 t[i+1] = lambda[i+1] ^ ALPHA_TO[MODNN(discr_r + b[i])];
188 else
189 t[i+1] = lambda[i+1];
190 }
191 if (2 * el <= r + no_eras - 1) {
192 el = r + no_eras - el;
193 /*
194 * 2 lines below: B(x) <-- inv(discr_r) *
195 * lambda(x)
196 */
197 for (i = 0; i <= NROOTS; i++)
198 b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
199 } else {
200 /* 2 lines below: B(x) <-- x*B(x) */
201 memmove(&b[1],b,NROOTS*sizeof(b[0]));
202 b[0] = A0;
203 }
204 memcpy(lambda,t,(NROOTS+1)*sizeof(t[0]));
205 }
206 }
207
208 /* Convert lambda to index form and compute deg(lambda(x)) */
209 deg_lambda = 0;
210 for(i=0;i<NROOTS+1;i++){
211 lambda[i] = INDEX_OF[lambda[i]];
212 if(lambda[i] != A0)
213 deg_lambda = i;
214 }
215 /* Find roots of the error+erasure locator polynomial by Chien search */
216 memcpy(&reg[1],&lambda[1],NROOTS*sizeof(reg[0]));
217 count = 0; /* Number of roots of lambda(x) */
218 for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
219 q = 1; /* lambda[0] is always 0 */
220 for (j = deg_lambda; j > 0; j--){
221 if (reg[j] != A0) {
222 reg[j] = MODNN(reg[j] + j);
223 q ^= ALPHA_TO[reg[j]];
224 }
225 }
226 if (q != 0)
227 continue; /* Not a root */
228 /* store root (index-form) and error location number */
229#if DEBUG>=2
230 printf("count %d root %d loc %d\n",count,i,k);
231#endif
232 root[count] = i;
233 loc[count] = k;
234 /* If we've already found max possible roots,
235 * abort the search to save time
236 */
237 if(++count == deg_lambda)
238 break;
239 }
240 if (deg_lambda != count) {
241 /*
242 * deg(lambda) unequal to number of roots => uncorrectable
243 * error detected
244 */
245 count = -1;
246 goto finish;
247 }
248 /*
249 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
250 * x**NROOTS). in index form. Also find deg(omega).
251 */
252 deg_omega = deg_lambda-1;
253 for (i = 0; i <= deg_omega;i++){
254 tmp = 0;
255 for(j=i;j >= 0; j--){
256 if ((s[i - j] != A0) && (lambda[j] != A0))
257 tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
258 }
259 omega[i] = INDEX_OF[tmp];
260 }
261
262 /*
263 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
264 * inv(X(l))**(FCR-1) and den = lambda_pr(inv(X(l))) all in poly-form
265 */
266 for (j = count-1; j >=0; j--) {
267 num1 = 0;
268 for (i = deg_omega; i >= 0; i--) {
269 if (omega[i] != A0)
270 num1 ^= ALPHA_TO[MODNN(omega[i] + i * root[j])];
271 }
272 num2 = ALPHA_TO[MODNN(root[j] * (FCR - 1) + NN)];
273 den = 0;
274
275 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
276 for (i = MIN(deg_lambda,NROOTS-1) & ~1; i >= 0; i -=2) {
277 if(lambda[i+1] != A0)
278 den ^= ALPHA_TO[MODNN(lambda[i+1] + i * root[j])];
279 }
280#if DEBUG >= 1
281 if (den == 0) {
282 printf("\n ERROR: denominator = 0\n");
283 count = -1;
284 goto finish;
285 }
286#endif
287 /* Apply error to data */
288 if (num1 != 0 && loc[j] >= PAD) {
289 data[loc[j]-PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])];
290 }
291 }
292 finish:
293 if(eras_pos != NULL){
294 for(i=0;i<count;i++)
295 eras_pos[i] = loc[i];
296 }
297 retval = count;
298}