GNU Radio's SATNOGS Package
decode_rs.h
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1 /* 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;
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];
80 
81  /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
82  for (i = 0; i < NROOTS; i++)
83  {
84  s[i] = data[0];
85  }
86 
87  for (j = 1; j < NN - PAD; j++)
88  {
89  for (i = 0; i < NROOTS; i++) {
90  if (s[i] == 0) {
91  s[i] = data[j];
92  }
93  else {
94  s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR + i) * PRIM)];
95  }
96  }
97  }
98 
99  /* Convert syndromes to index form, checking for nonzero condition */
100  syn_error = 0;
101  for (i = 0; i < NROOTS; i++)
102  {
103  syn_error |= s[i];
104  s[i] = INDEX_OF[s[i]];
105  }
106 
107  if (!syn_error)
108  {
109  /* if syndrome is zero, data[] is a codeword and there are no
110  * errors to correct. So return data[] unmodified
111  */
112  count = 0;
113  goto finish;
114  }
115  memset(&lambda[1], 0, NROOTS * sizeof(lambda[0]));
116  lambda[0] = 1;
117 
118  if (no_eras > 0)
119  {
120  /* Init lambda to be the erasure locator polynomial */
121  lambda[1] = ALPHA_TO[MODNN(PRIM * (NN - 1 - eras_pos[0]))];
122  for (i = 1; i < no_eras; i++) {
123  u = MODNN(PRIM * (NN - 1 - eras_pos[i]));
124  for (j = i + 1; j > 0; j--) {
125  tmp = INDEX_OF[lambda[j - 1]];
126  if (tmp != A0) {
127  lambda[j] ^= ALPHA_TO[MODNN(u + tmp)];
128  }
129  }
130  }
131 
132 #if DEBUG >= 1
133  /* Test code that verifies the erasure locator polynomial just constructed
134  Needed only for decoder debugging. */
135 
136  /* find roots of the erasure location polynomial */
137  for (i = 1; i <= no_eras; i++) {
138  reg[i] = INDEX_OF[lambda[i]];
139  }
140 
141  count = 0;
142  for (i = 1, k = IPRIM - 1; i <= NN; i++, k = MODNN(k + IPRIM)) {
143  q = 1;
144  for (j = 1; j <= no_eras; j++)
145  if (reg[j] != A0) {
146  reg[j] = MODNN(reg[j] + j);
147  q ^= ALPHA_TO[reg[j]];
148  }
149  if (q != 0) {
150  continue;
151  }
152  /* store root and error location number indices */
153  root[count] = i;
154  loc[count] = k;
155  count++;
156  }
157  if (count != no_eras) {
158  printf("count = %d no_eras = %d\n lambda(x) is WRONG\n", count, no_eras);
159  count = -1;
160  goto finish;
161  }
162 #if DEBUG >= 2
163  printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
164  for (i = 0; i < count; i++) {
165  printf("%d ", loc[i]);
166  }
167  printf("\n");
168 #endif
169 #endif
170  }
171  for (i = 0; i < NROOTS + 1; i++)
172  {
173  b[i] = INDEX_OF[lambda[i]];
174  }
175 
176  /*
177  * Begin Berlekamp-Massey algorithm to determine error+erasure
178  * locator polynomial
179  */
180  r = no_eras;
181  el = no_eras;
182  while (++r <= NROOTS) /* r is the step number */
183  {
184  /* Compute discrepancy at the r-th step in poly-form */
185  discr_r = 0;
186  for (i = 0; i < r; i++) {
187  if ((lambda[i] != 0) && (s[r - i - 1] != A0)) {
188  discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r - i - 1])];
189  }
190  }
191  discr_r = INDEX_OF[discr_r]; /* Index form */
192  if (discr_r == A0) {
193  /* 2 lines below: B(x) <-- x*B(x) */
194  memmove(&b[1], b, NROOTS * sizeof(b[0]));
195  b[0] = A0;
196  }
197  else {
198  /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
199  t[0] = lambda[0];
200  for (i = 0 ; i < NROOTS; i++) {
201  if (b[i] != A0) {
202  t[i + 1] = lambda[i + 1] ^ ALPHA_TO[MODNN(discr_r + b[i])];
203  }
204  else {
205  t[i + 1] = lambda[i + 1];
206  }
207  }
208  if (2 * el <= r + no_eras - 1) {
209  el = r + no_eras - el;
210  /*
211  * 2 lines below: B(x) <-- inv(discr_r) *
212  * lambda(x)
213  */
214  for (i = 0; i <= NROOTS; i++) {
215  b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
216  }
217  }
218  else {
219  /* 2 lines below: B(x) <-- x*B(x) */
220  memmove(&b[1], b, NROOTS * sizeof(b[0]));
221  b[0] = A0;
222  }
223  memcpy(lambda, t, (NROOTS + 1)*sizeof(t[0]));
224  }
225  }
226 
227  /* Convert lambda to index form and compute deg(lambda(x)) */
228  deg_lambda = 0;
229  for (i = 0; i < NROOTS + 1; i++)
230  {
231  lambda[i] = INDEX_OF[lambda[i]];
232  if (lambda[i] != A0) {
233  deg_lambda = i;
234  }
235  }
236  /* Find roots of the error+erasure locator polynomial by Chien search */
237  memcpy(&reg[1], &lambda[1], NROOTS * sizeof(reg[0]));
238  count = 0; /* Number of roots of lambda(x) */
239  for (i = 1, k = IPRIM - 1; i <= NN; i++, k = MODNN(k + IPRIM))
240  {
241  q = 1; /* lambda[0] is always 0 */
242  for (j = deg_lambda; j > 0; j--) {
243  if (reg[j] != A0) {
244  reg[j] = MODNN(reg[j] + j);
245  q ^= ALPHA_TO[reg[j]];
246  }
247  }
248  if (q != 0) {
249  continue; /* Not a root */
250  }
251  /* store root (index-form) and error location number */
252 #if DEBUG>=2
253  printf("count %d root %d loc %d\n", count, i, k);
254 #endif
255  root[count] = i;
256  loc[count] = k;
257  /* If we've already found max possible roots,
258  * abort the search to save time
259  */
260  if (++count == deg_lambda) {
261  break;
262  }
263  }
264  if (deg_lambda != count)
265  {
266  /*
267  * deg(lambda) unequal to number of roots => uncorrectable
268  * error detected
269  */
270  count = -1;
271  goto finish;
272  }
273  /*
274  * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
275  * x**NROOTS). in index form. Also find deg(omega).
276  */
277  deg_omega = deg_lambda - 1;
278  for (i = 0; i <= deg_omega; i++)
279  {
280  tmp = 0;
281  for (j = i; j >= 0; j--) {
282  if ((s[i - j] != A0) && (lambda[j] != A0)) {
283  tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
284  }
285  }
286  omega[i] = INDEX_OF[tmp];
287  }
288 
289  /*
290  * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
291  * inv(X(l))**(FCR-1) and den = lambda_pr(inv(X(l))) all in poly-form
292  */
293  for (j = count - 1; j >= 0; j--)
294  {
295  num1 = 0;
296  for (i = deg_omega; i >= 0; i--) {
297  if (omega[i] != A0) {
298  num1 ^= ALPHA_TO[MODNN(omega[i] + i * root[j])];
299  }
300  }
301  num2 = ALPHA_TO[MODNN(root[j] * (FCR - 1) + NN)];
302  den = 0;
303 
304  /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
305  for (i = MIN(deg_lambda, NROOTS - 1) & ~1; i >= 0; i -= 2) {
306  if (lambda[i + 1] != A0) {
307  den ^= ALPHA_TO[MODNN(lambda[i + 1] + i * root[j])];
308  }
309  }
310 #if DEBUG >= 1
311  if (den == 0) {
312  printf("\n ERROR: denominator = 0\n");
313  count = -1;
314  goto finish;
315  }
316 #endif
317  /* Apply error to data */
318  if (num1 != 0 && loc[j] >= PAD) {
319  data[loc[j] - PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN -
320  INDEX_OF[den])];
321  }
322  }
323 finish:
324  if (eras_pos != NULL)
325  {
326  for (i = 0; i < count; i++) {
327  eras_pos[i] = loc[i];
328  }
329  }
330  retval = count;
331 }
int r
Definition: decode_rs.h:71
data_t t[NROOTS+1]
Definition: decode_rs.h:77
int i
Definition: decode_rs.h:71
int j
Definition: decode_rs.h:71
data_t num2
Definition: decode_rs.h:74
int count
Definition: decode_rs.h:79
data_t q
Definition: decode_rs.h:74
data_t root[NROOTS]
Definition: decode_rs.h:78
memset(parity, 0, NROOTS *sizeof(data_t))
#define PAD
Definition: char.h:19
data_t lambda[NROOTS+1]
Definition: decode_rs.h:75
#define NULL
Definition: decode_rs.h:63
#define NN
Definition: ccsds.h:3
deg_lambda
Definition: decode_rs.h:228
unsigned char data_t
Definition: ccsds.h:1
#define FCR
Definition: char.h:16
#define INDEX_OF
Definition: char.h:13
data_t omega[NROOTS+1]
Definition: decode_rs.h:77
data_t discr_r
Definition: decode_rs.h:74
data_t reg[NROOTS+1]
Definition: decode_rs.h:78
data_t tmp
Definition: decode_rs.h:74
data_t b[NROOTS+1]
Definition: decode_rs.h:77
#define ALPHA_TO
Definition: char.h:12
#define NROOTS
Definition: ccsds.h:4
#define A0
Definition: decode_rs.h:69
#define MIN(a, b)
Definition: decode_rs.h:67
deg_omega
Definition: decode_rs.h:277
data_t loc[NROOTS]
Definition: decode_rs.h:78
#define MODNN(x)
Definition: char.h:8
data_t den
Definition: decode_rs.h:74
data_t num1
Definition: decode_rs.h:74
#define IPRIM
Definition: char.h:18
#define PRIM
Definition: char.h:17
data_t u
Definition: decode_rs.h:74
int k
Definition: decode_rs.h:71
data_t s[NROOTS]
Definition: decode_rs.h:75
int syn_error
Definition: decode_rs.h:79
el
Definition: decode_rs.h:181