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-rw-r--r--src/fec/decode_rs.h298
1 files changed, 0 insertions, 298 deletions
diff --git a/src/fec/decode_rs.h b/src/fec/decode_rs.h
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--- a/src/fec/decode_rs.h
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-/* 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;
-}
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