aboutsummaryrefslogtreecommitdiffstats
path: root/contrib/fec/decode_rs.h
blob: c165cf3de939adba4c02625c9c58c781e293d6ac (plain)
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
/* The guts of the Reed-Solomon decoder, meant to be #included
 * into a function body with the following typedefs, macros and variables supplied
 * according to the code parameters:

 * data_t - a typedef for the data symbol
 * data_t data[] - array of NN data and parity symbols to be corrected in place
 * retval - an integer lvalue into which the decoder's return code is written
 * NROOTS - the number of roots in the RS code generator polynomial,
 *          which is the same as the number of parity symbols in a block.
            Integer variable or literal.
 * NN - the total number of symbols in a RS block. Integer variable or literal.
 * PAD - the number of pad symbols in a block. Integer variable or literal.
 * ALPHA_TO - The address of an array of NN elements to convert Galois field
 *            elements in index (log) form to polynomial form. Read only.
 * INDEX_OF - The address of an array of NN elements to convert Galois field
 *            elements in polynomial form to index (log) form. Read only.
 * MODNN - a function to reduce its argument modulo NN. May be inline or a macro.
 * FCR - An integer literal or variable specifying the first consecutive root of the
 *       Reed-Solomon generator polynomial. Integer variable or literal.
 * PRIM - The primitive root of the generator poly. Integer variable or literal.
 * DEBUG - If set to 1 or more, do various internal consistency checking. Leave this
 *         undefined for production code

 * The memset(), memmove(), and memcpy() functions are used. The appropriate header
 * file declaring these functions (usually <string.h>) must be included by the calling
 * program.
 */


#if !defined(NROOTS)
#error "NROOTS not defined"
#endif

#if !defined(NN)
#error "NN not defined"
#endif

#if !defined(PAD)
#error "PAD not defined"
#endif

#if !defined(ALPHA_TO)
#error "ALPHA_TO not defined"
#endif

#if !defined(INDEX_OF)
#error "INDEX_OF not defined"
#endif

#if !defined(MODNN)
#error "MODNN not defined"
#endif

#if !defined(FCR)
#error "FCR not defined"
#endif

#if !defined(PRIM)
#error "PRIM not defined"
#endif

#if !defined(NULL)
#define NULL ((void *)0)
#endif

#undef MIN
#define	MIN(a,b)	((a) < (b) ? (a) : (b))
#undef A0
#define A0 (NN)

{
  int deg_lambda, el, deg_omega;
  int i, j, r,k;
  data_t u,q,tmp,num1,num2,den,discr_r;
  data_t lambda[NROOTS+1], s[NROOTS];	/* Err+Eras Locator poly
					 * and syndrome poly */
  data_t b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1];
  data_t root[NROOTS], reg[NROOTS+1], loc[NROOTS];
  int syn_error, count;

  /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
  for(i=0;i<NROOTS;i++)
    s[i] = data[0];

  for(j=1;j<NN-PAD;j++){
    for(i=0;i<NROOTS;i++){
      if(s[i] == 0){
	s[i] = data[j];
      } else {
	s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR+i)*PRIM)];
      }
    }
  }

  /* Convert syndromes to index form, checking for nonzero condition */
  syn_error = 0;
  for(i=0;i<NROOTS;i++){
    syn_error |= s[i];
    s[i] = INDEX_OF[s[i]];
  }

  if (!syn_error) {
    /* if syndrome is zero, data[] is a codeword and there are no
     * errors to correct. So return data[] unmodified
     */
    count = 0;
    goto finish;
  }
  memset(&lambda[1],0,NROOTS*sizeof(lambda[0]));
  lambda[0] = 1;

  if (no_eras > 0) {
    /* Init lambda to be the erasure locator polynomial */
    lambda[1] = ALPHA_TO[MODNN(PRIM*(NN-1-eras_pos[0]))];
    for (i = 1; i < no_eras; i++) {
      u = MODNN(PRIM*(NN-1-eras_pos[i]));
      for (j = i+1; j > 0; j--) {
	tmp = INDEX_OF[lambda[j - 1]];
	if(tmp != A0)
	  lambda[j] ^= ALPHA_TO[MODNN(u + tmp)];
      }
    }

#if DEBUG >= 1
    /* Test code that verifies the erasure locator polynomial just constructed
       Needed only for decoder debugging. */
    
    /* find roots of the erasure location polynomial */
    for(i=1;i<=no_eras;i++)
      reg[i] = INDEX_OF[lambda[i]];

    count = 0;
    for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
      q = 1;
      for (j = 1; j <= no_eras; j++)
	if (reg[j] != A0) {
	  reg[j] = MODNN(reg[j] + j);
	  q ^= ALPHA_TO[reg[j]];
	}
      if (q != 0)
	continue;
      /* store root and error location number indices */
      root[count] = i;
      loc[count] = k;
      count++;
    }
    if (count != no_eras) {
      printf("count = %d no_eras = %d\n lambda(x) is WRONG\n",count,no_eras);
      count = -1;
      goto finish;
    }
#if DEBUG >= 2
    printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
    for (i = 0; i < count; i++)
      printf("%d ", loc[i]);
    printf("\n");
#endif
#endif
  }
  for(i=0;i<NROOTS+1;i++)
    b[i] = INDEX_OF[lambda[i]];
  
  /*
   * Begin Berlekamp-Massey algorithm to determine error+erasure
   * locator polynomial
   */
  r = no_eras;
  el = no_eras;
  while (++r <= NROOTS) {	/* r is the step number */
    /* Compute discrepancy at the r-th step in poly-form */
    discr_r = 0;
    for (i = 0; i < r; i++){
      if ((lambda[i] != 0) && (s[r-i-1] != A0)) {
	discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r-i-1])];
      }
    }
    discr_r = INDEX_OF[discr_r];	/* Index form */
    if (discr_r == A0) {
      /* 2 lines below: B(x) <-- x*B(x) */
      memmove(&b[1],b,NROOTS*sizeof(b[0]));
      b[0] = A0;
    } else {
      /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
      t[0] = lambda[0];
      for (i = 0 ; i < NROOTS; i++) {
	if(b[i] != A0)
	  t[i+1] = lambda[i+1] ^ ALPHA_TO[MODNN(discr_r + b[i])];
	else
	  t[i+1] = lambda[i+1];
      }
      if (2 * el <= r + no_eras - 1) {
	el = r + no_eras - el;
	/*
	 * 2 lines below: B(x) <-- inv(discr_r) *
	 * lambda(x)
	 */
	for (i = 0; i <= NROOTS; i++)
	  b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
      } else {
	/* 2 lines below: B(x) <-- x*B(x) */
	memmove(&b[1],b,NROOTS*sizeof(b[0]));
	b[0] = A0;
      }
      memcpy(lambda,t,(NROOTS+1)*sizeof(t[0]));
    }
  }

  /* Convert lambda to index form and compute deg(lambda(x)) */
  deg_lambda = 0;
  for(i=0;i<NROOTS+1;i++){
    lambda[i] = INDEX_OF[lambda[i]];
    if(lambda[i] != A0)
      deg_lambda = i;
  }
  /* Find roots of the error+erasure locator polynomial by Chien search */
  memcpy(&reg[1],&lambda[1],NROOTS*sizeof(reg[0]));
  count = 0;		/* Number of roots of lambda(x) */
  for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
    q = 1; /* lambda[0] is always 0 */
    for (j = deg_lambda; j > 0; j--){
      if (reg[j] != A0) {
	reg[j] = MODNN(reg[j] + j);
	q ^= ALPHA_TO[reg[j]];
      }
    }
    if (q != 0)
      continue; /* Not a root */
    /* store root (index-form) and error location number */
#if DEBUG>=2
    printf("count %d root %d loc %d\n",count,i,k);
#endif
    root[count] = i;
    loc[count] = k;
    /* If we've already found max possible roots,
     * abort the search to save time
     */
    if(++count == deg_lambda)
      break;
  }
  if (deg_lambda != count) {
    /*
     * deg(lambda) unequal to number of roots => uncorrectable
     * error detected
     */
    count = -1;
    goto finish;
  }
  /*
   * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
   * x**NROOTS). in index form. Also find deg(omega).
   */
  deg_omega = deg_lambda-1;
  for (i = 0; i <= deg_omega;i++){
    tmp = 0;
    for(j=i;j >= 0; j--){
      if ((s[i - j] != A0) && (lambda[j] != A0))
	tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
    }
    omega[i] = INDEX_OF[tmp];
  }

  /*
   * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
   * inv(X(l))**(FCR-1) and den = lambda_pr(inv(X(l))) all in poly-form
   */
  for (j = count-1; j >=0; j--) {
    num1 = 0;
    for (i = deg_omega; i >= 0; i--) {
      if (omega[i] != A0)
	num1  ^= ALPHA_TO[MODNN(omega[i] + i * root[j])];
    }
    num2 = ALPHA_TO[MODNN(root[j] * (FCR - 1) + NN)];
    den = 0;
    
    /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
    for (i = MIN(deg_lambda,NROOTS-1) & ~1; i >= 0; i -=2) {
      if(lambda[i+1] != A0)
	den ^= ALPHA_TO[MODNN(lambda[i+1] + i * root[j])];
    }
#if DEBUG >= 1
    if (den == 0) {
      printf("\n ERROR: denominator = 0\n");
      count = -1;
      goto finish;
    }
#endif
    /* Apply error to data */
    if (num1 != 0 && loc[j] >= PAD) {
      data[loc[j]-PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])];
    }
  }
 finish:
  if(eras_pos != NULL){
    for(i=0;i<count;i++)
      eras_pos[i] = loc[i];
  }
  retval = count;
}