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 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
