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Diffstat (limited to 'src/fec/decode_rs.h')
-rw-r--r-- | src/fec/decode_rs.h | 298 |
1 files changed, 298 insertions, 0 deletions
diff --git a/src/fec/decode_rs.h b/src/fec/decode_rs.h new file mode 100644 index 0000000..c165cf3 --- /dev/null +++ b/src/fec/decode_rs.h @@ -0,0 +1,298 @@ +/* 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(®[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; +} |