GNU Radio's SATELLITES Package

lib/libfec/decode_rs.h
Go to the documentation of this file.
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;
74 data_t u, q, tmp, num1, num2, den, discr_r;
75#ifdef MAX_ARRAY
76 data_t lambda[MAX_ARRAY], s[MAX_ARRAY]; /* Err+Eras Locator poly
77 * and syndrome poly */
78 data_t b[MAX_ARRAY], t[MAX_ARRAY], omega[MAX_ARRAY];
79 data_t root[MAX_ARRAY], reg[MAX_ARRAY], loc[MAX_ARRAY];
80#else /* MAX_ARRAY */
81 data_t lambda[NROOTS + 1], s[NROOTS]; /* Err+Eras Locator poly
82 * and syndrome poly */
83 data_t b[NROOTS + 1], t[NROOTS + 1], omega[NROOTS + 1];
84 data_t root[NROOTS], reg[NROOTS + 1], loc[NROOTS];
85#endif /* MAX_ARRAY */
86 int syn_error, count;
87
88 /* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
89 for (i = 0; i < NROOTS; i++)
90 s[i] = data[0];
91
92 for (j = 1; j < NN - PAD; j++) {
93 for (i = 0; i < NROOTS; i++) {
94 if (s[i] == 0) {
95 s[i] = data[j];
96 } else {
97 s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR + i) * PRIM)];
98 }
99 }
100 }
101
102 /* Convert syndromes to index form, checking for nonzero condition */
103 syn_error = 0;
104 for (i = 0; i < NROOTS; i++) {
105 syn_error |= s[i];
106 s[i] = INDEX_OF[s[i]];
107 }
108
109 if (!syn_error) {
110 /* if syndrome is zero, data[] is a codeword and there are no
111 * errors to correct. So return data[] unmodified
112 */
113 count = 0;
114 goto finish;
115 }
116 memset(&lambda[1], 0, NROOTS * sizeof(lambda[0]));
117 lambda[0] = 1;
118
119 if (no_eras > 0) {
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#if DEBUG >= 1
132 /* Test code that verifies the erasure locator polynomial just constructed
133 Needed only for decoder debugging. */
134
135 /* find roots of the erasure location polynomial */
136 for (i = 1; i <= no_eras; i++)
137 reg[i] = INDEX_OF[lambda[i]];
138
139 count = 0;
140 for (i = 1, k = IPRIM - 1; i <= NN; i++, k = MODNN(k + IPRIM)) {
141 q = 1;
142 for (j = 1; j <= no_eras; j++)
143 if (reg[j] != A0) {
144 reg[j] = MODNN(reg[j] + j);
145 q ^= ALPHA_TO[reg[j]];
146 }
147 if (q != 0)
148 continue;
149 /* store root and error location number indices */
150 root[count] = i;
151 loc[count] = k;
152 count++;
153 }
154 if (count != no_eras) {
155 printf("count = %d no_eras = %d\n lambda(x) is WRONG\n", count, no_eras);
156 count = -1;
157 goto finish;
158 }
159#if DEBUG >= 2
160 printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
161 for (i = 0; i < count; i++)
162 printf("%d ", loc[i]);
163 printf("\n");
164#endif
165#endif
166 }
167 for (i = 0; i < NROOTS + 1; i++)
168 b[i] = INDEX_OF[lambda[i]];
169
170 /*
171 * Begin Berlekamp-Massey algorithm to determine error+erasure
172 * locator polynomial
173 */
174 r = no_eras;
175 el = no_eras;
176 while (++r <= NROOTS) { /* r is the step number */
177 /* Compute discrepancy at the r-th step in poly-form */
178 discr_r = 0;
179 for (i = 0; i < r; i++) {
180 if ((lambda[i] != 0) && (s[r - i - 1] != A0)) {
181 discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r - i - 1])];
182 }
183 }
184 discr_r = INDEX_OF[discr_r]; /* Index form */
185 if (discr_r == A0) {
186 /* 2 lines below: B(x) <-- x*B(x) */
187 memmove(&b[1], b, NROOTS * sizeof(b[0]));
188 b[0] = A0;
189 } else {
190 /* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
191 t[0] = lambda[0];
192 for (i = 0; i < NROOTS; i++) {
193 if (b[i] != A0)
194 t[i + 1] = lambda[i + 1] ^ ALPHA_TO[MODNN(discr_r + b[i])];
195 else
196 t[i + 1] = lambda[i + 1];
197 }
198 if (2 * el <= r + no_eras - 1) {
199 el = r + no_eras - el;
200 /*
201 * 2 lines below: B(x) <-- inv(discr_r) *
202 * lambda(x)
203 */
204 for (i = 0; i <= NROOTS; i++)
205 b[i] =
206 (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
207 } else {
208 /* 2 lines below: B(x) <-- x*B(x) */
209 memmove(&b[1], b, NROOTS * sizeof(b[0]));
210 b[0] = A0;
211 }
212 memcpy(lambda, t, (NROOTS + 1) * sizeof(t[0]));
213 }
214 }
215
216 /* Convert lambda to index form and compute deg(lambda(x)) */
217 deg_lambda = 0;
218 for (i = 0; i < NROOTS + 1; i++) {
219 lambda[i] = INDEX_OF[lambda[i]];
220 if (lambda[i] != A0)
221 deg_lambda = i;
222 }
223 /* Find roots of the error+erasure locator polynomial by Chien search */
224 memcpy(&reg[1], &lambda[1], NROOTS * sizeof(reg[0]));
225 count = 0; /* Number of roots of lambda(x) */
226 for (i = 1, k = IPRIM - 1; i <= NN; i++, k = MODNN(k + IPRIM)) {
227 q = 1; /* lambda[0] is always 0 */
228 for (j = deg_lambda; j > 0; j--) {
229 if (reg[j] != A0) {
230 reg[j] = MODNN(reg[j] + j);
231 q ^= ALPHA_TO[reg[j]];
232 }
233 }
234 if (q != 0)
235 continue; /* Not a root */
236 /* store root (index-form) and error location number */
237#if DEBUG >= 2
238 printf("count %d root %d loc %d\n", count, i, k);
239#endif
240 root[count] = i;
241 loc[count] = k;
242 /* If we've already found max possible roots,
243 * abort the search to save time
244 */
245 if (++count == deg_lambda)
246 break;
247 }
248 if (deg_lambda != count) {
249 /*
250 * deg(lambda) unequal to number of roots => uncorrectable
251 * error detected
252 */
253 count = -1;
254 goto finish;
255 }
256 /*
257 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
258 * x**NROOTS). in index form. Also find deg(omega).
259 */
260 deg_omega = deg_lambda - 1;
261 for (i = 0; i <= deg_omega; i++) {
262 tmp = 0;
263 for (j = i; j >= 0; j--) {
264 if ((s[i - j] != A0) && (lambda[j] != A0))
265 tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
266 }
267 omega[i] = INDEX_OF[tmp];
268 }
269
270 /*
271 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
272 * inv(X(l))**(FCR-1) and den = lambda_pr(inv(X(l))) all in poly-form
273 */
274 for (j = count - 1; j >= 0; j--) {
275 num1 = 0;
276 for (i = deg_omega; i >= 0; i--) {
277 if (omega[i] != A0)
278 num1 ^= ALPHA_TO[MODNN(omega[i] + i * root[j])];
279 }
280 num2 = ALPHA_TO[MODNN(root[j] * (FCR - 1) + NN)];
281 den = 0;
282
283 /* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
284 for (i = MIN(deg_lambda, NROOTS - 1) & ~1; i >= 0; i -= 2) {
285 if (lambda[i + 1] != A0)
286 den ^= ALPHA_TO[MODNN(lambda[i + 1] + i * root[j])];
287 }
288#if DEBUG >= 1
289 if (den == 0) {
290 printf("\n ERROR: denominator = 0\n");
291 count = -1;
292 goto finish;
293 }
294#endif
295 /* Apply error to data */
296 if (num1 != 0 && loc[j] >= PAD) {
297 data[loc[j] - PAD] ^=
298 ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])];
299 }
300 }
301finish:
302 if (eras_pos != NULL) {
303 for (i = 0; i < count; i++)
304 eras_pos[i] = loc[i];
305 }
306 retval = count;
307}
NN
#define NN
Definition ccsds.h:3
NROOTS
#define NROOTS
Definition ccsds.h:4
data_t
unsigned char data_t
Definition ccsds.h:1
A0
#define A0
Definition char.h:20
FCR
#define FCR
Definition char.h:16
PAD
#define PAD
Definition char.h:19
MODNN
#define MODNN(x)
Definition char.h:8
INDEX_OF
#define INDEX_OF
Definition char.h:13
PRIM
#define PRIM
Definition char.h:17
IPRIM
#define IPRIM
Definition char.h:18
ALPHA_TO
#define ALPHA_TO
Definition char.h:12
q
data_t q
Definition lib/libfec/decode_rs.h:74
NULL
#define NULL
Definition lib/libfec/decode_rs.h:63
num2
data_t num2
Definition lib/libfec/decode_rs.h:74
lambda
data_t lambda[NROOTS+1]
Definition lib/libfec/decode_rs.h:81
num1
data_t num1
Definition lib/libfec/decode_rs.h:74
reg
data_t reg[NROOTS+1]
Definition lib/libfec/decode_rs.h:84
loc
data_t loc[NROOTS]
Definition lib/libfec/decode_rs.h:84
j
int j
Definition lib/libfec/decode_rs.h:73
MIN
#define MIN(a, b)
Definition lib/libfec/decode_rs.h:67
syn_error
int syn_error
Definition lib/libfec/decode_rs.h:86
r
int r
Definition lib/libfec/decode_rs.h:73
den
data_t den
Definition lib/libfec/decode_rs.h:74
deg_omega
deg_omega
Definition lib/libfec/decode_rs.h:260
discr_r
data_t discr_r
Definition lib/libfec/decode_rs.h:74
el
el
Definition lib/libfec/decode_rs.h:175
s
data_t s[NROOTS]
Definition lib/libfec/decode_rs.h:81
u
data_t u
Definition lib/libfec/decode_rs.h:74
tmp
data_t tmp
Definition lib/libfec/decode_rs.h:74
t
data_t t[NROOTS+1]
Definition lib/libfec/decode_rs.h:83
k
int k
Definition lib/libfec/decode_rs.h:73
i
int i
Definition lib/libfec/decode_rs.h:73
omega
data_t omega[NROOTS+1]
Definition lib/libfec/decode_rs.h:83
root
data_t root[NROOTS]
Definition lib/libfec/decode_rs.h:84
count
int count
Definition lib/libfec/decode_rs.h:86
deg_lambda
deg_lambda
Definition lib/libfec/decode_rs.h:217
b
data_t b[NROOTS+1]
Definition lib/libfec/decode_rs.h:83
memset
memset(parity, 0, NROOTS *sizeof(data_t))