ocssw V2020
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 */
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)) */
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  */
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) {
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 }
#define INDEX_OF
Definition: fec_seahawk.c:44
data_t q
Definition: decode_rs.h:74
int r
Definition: decode_rs.h:73
data_t t[NROOTS+1]
Definition: decode_rs.h:77
data_t num2
Definition: decode_rs.h:74
int j
Definition: decode_rs.h:73
#define IPRIM
Definition: fec_seahawk.c:49
data_t root[NROOTS]
Definition: decode_rs.h:78
#define FCR
Definition: fec_seahawk.c:47
#define NULL
Definition: decode_rs.h:63
int NN
Definition: Usds.c:61
data_t lambda[NROOTS+1]
Definition: decode_rs.h:75
#define NROOTS
Definition: ccsds.h:4
#define PAD
Definition: fec_seahawk.c:50
deg_lambda
Definition: decode_rs.h:209
unsigned char data_t
Definition: ccsds.h:1
#define PRIM
Definition: fec_seahawk.c:48
data_t tmp
Definition: decode_rs.h:74
data_t omega[NROOTS+1]
Definition: decode_rs.h:77
#define A0
Definition: decode_rs.h:69
no change in intended resolving MODur00064 Corrected handling of bad ephemeris attitude data
Definition: HISTORY.txt:356
data_t discr_r
Definition: decode_rs.h:74
data_t reg[NROOTS+1]
Definition: decode_rs.h:78
data_t b[NROOTS+1]
Definition: decode_rs.h:77
data_t loc[NROOTS]
Definition: decode_rs.h:78
data_t num1
Definition: decode_rs.h:74
data_t u
Definition: decode_rs.h:74
#define MIN(a, b)
Definition: decode_rs.h:67
deg_omega
Definition: decode_rs.h:252
data_t den
Definition: decode_rs.h:74
#define MODNN(x)
Definition: fec_seahawk.c:35
data_t s[NROOTS]
Definition: decode_rs.h:75
int syn_error
Definition: decode_rs.h:79
#define ALPHA_TO
Definition: fec_seahawk.c:43
int i
Definition: decode_rs.h:71
int k
Definition: decode_rs.h:73
el
Definition: decode_rs.h:168
int count
Definition: decode_rs.h:79