mirror of
https://github.com/servalproject/serval-dna.git
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299 lines
8.2 KiB
C
299 lines
8.2 KiB
C
/* The guts of the Reed-Solomon decoder, meant to be #included
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* into a function body with the following typedefs, macros and variables supplied
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* according to the code parameters:
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* data_t - a typedef for the data symbol
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* data_t data[] - array of NN data and parity symbols to be corrected in place
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* retval - an integer lvalue into which the decoder's return code is written
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* NROOTS - the number of roots in the RS code generator polynomial,
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* which is the same as the number of parity symbols in a block.
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Integer variable or literal.
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* NN - the total number of symbols in a RS block. Integer variable or literal.
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* PAD - the number of pad symbols in a block. Integer variable or literal.
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* ALPHA_TO - The address of an array of NN elements to convert Galois field
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* elements in index (log) form to polynomial form. Read only.
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* INDEX_OF - The address of an array of NN elements to convert Galois field
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* elements in polynomial form to index (log) form. Read only.
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* MODNN - a function to reduce its argument modulo NN. May be inline or a macro.
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* FCR - An integer literal or variable specifying the first consecutive root of the
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* Reed-Solomon generator polynomial. Integer variable or literal.
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* PRIM - The primitive root of the generator poly. Integer variable or literal.
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* DEBUG - If set to 1 or more, do various internal consistency checking. Leave this
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* undefined for production code
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* The memset(), memmove(), and memcpy() functions are used. The appropriate header
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* file declaring these functions (usually <string.h>) must be included by the calling
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* program.
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*/
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#if !defined(NROOTS)
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#error "NROOTS not defined"
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#endif
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#if !defined(NN)
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#error "NN not defined"
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#endif
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#if !defined(PAD)
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#error "PAD not defined"
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#endif
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#if !defined(ALPHA_TO)
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#error "ALPHA_TO not defined"
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#endif
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#if !defined(INDEX_OF)
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#error "INDEX_OF not defined"
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#endif
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#if !defined(MODNN)
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#error "MODNN not defined"
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#endif
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#if !defined(FCR)
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#error "FCR not defined"
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#endif
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#if !defined(PRIM)
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#error "PRIM not defined"
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#endif
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#if !defined(NULL)
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#define NULL ((void *)0)
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#endif
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#undef MIN
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#define MIN(a,b) ((a) < (b) ? (a) : (b))
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#undef A0
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#define A0 (NN)
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{
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int deg_lambda, el, deg_omega;
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int i, j, r,k;
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data_t u,q,tmp,num1,num2,den,discr_r;
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data_t lambda[NROOTS+1], s[NROOTS]; /* Err+Eras Locator poly
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* and syndrome poly */
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data_t b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1];
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data_t root[NROOTS], reg[NROOTS+1], loc[NROOTS];
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int syn_error, count;
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/* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
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for(i=0;i<NROOTS;i++)
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s[i] = data[0];
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for(j=1;j<NN-PAD;j++){
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for(i=0;i<NROOTS;i++){
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if(s[i] == 0){
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s[i] = data[j];
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} else {
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s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR+i)*PRIM)];
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}
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}
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}
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/* Convert syndromes to index form, checking for nonzero condition */
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syn_error = 0;
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for(i=0;i<NROOTS;i++){
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syn_error |= s[i];
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s[i] = INDEX_OF[s[i]];
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}
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if (!syn_error) {
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/* if syndrome is zero, data[] is a codeword and there are no
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* errors to correct. So return data[] unmodified
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*/
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count = 0;
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goto finish;
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}
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memset(&lambda[1],0,NROOTS*sizeof(lambda[0]));
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lambda[0] = 1;
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if (no_eras > 0) {
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/* Init lambda to be the erasure locator polynomial */
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lambda[1] = ALPHA_TO[MODNN(PRIM*(NN-1-eras_pos[0]))];
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for (i = 1; i < no_eras; i++) {
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u = MODNN(PRIM*(NN-1-eras_pos[i]));
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for (j = i+1; j > 0; j--) {
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tmp = INDEX_OF[lambda[j - 1]];
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if(tmp != A0)
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lambda[j] ^= ALPHA_TO[MODNN(u + tmp)];
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}
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}
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#if DEBUG >= 1
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/* Test code that verifies the erasure locator polynomial just constructed
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Needed only for decoder debugging. */
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/* find roots of the erasure location polynomial */
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for(i=1;i<=no_eras;i++)
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reg[i] = INDEX_OF[lambda[i]];
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count = 0;
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for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
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q = 1;
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for (j = 1; j <= no_eras; j++)
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if (reg[j] != A0) {
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reg[j] = MODNN(reg[j] + j);
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q ^= ALPHA_TO[reg[j]];
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}
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if (q != 0)
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continue;
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/* store root and error location number indices */
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root[count] = i;
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loc[count] = k;
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count++;
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}
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if (count != no_eras) {
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printf("count = %d no_eras = %d\n lambda(x) is WRONG\n",count,no_eras);
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count = -1;
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goto finish;
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}
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#if DEBUG >= 2
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printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
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for (i = 0; i < count; i++)
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printf("%d ", loc[i]);
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printf("\n");
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#endif
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#endif
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}
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for(i=0;i<NROOTS+1;i++)
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b[i] = INDEX_OF[lambda[i]];
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/*
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* Begin Berlekamp-Massey algorithm to determine error+erasure
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* locator polynomial
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*/
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r = no_eras;
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el = no_eras;
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while (++r <= NROOTS) { /* r is the step number */
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/* Compute discrepancy at the r-th step in poly-form */
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discr_r = 0;
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for (i = 0; i < r; i++){
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if ((lambda[i] != 0) && (s[r-i-1] != A0)) {
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discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r-i-1])];
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}
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}
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discr_r = INDEX_OF[discr_r]; /* Index form */
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if (discr_r == A0) {
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/* 2 lines below: B(x) <-- x*B(x) */
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memmove(&b[1],b,NROOTS*sizeof(b[0]));
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b[0] = A0;
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} else {
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/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
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t[0] = lambda[0];
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for (i = 0 ; i < NROOTS; i++) {
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if(b[i] != A0)
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t[i+1] = lambda[i+1] ^ ALPHA_TO[MODNN(discr_r + b[i])];
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else
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t[i+1] = lambda[i+1];
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}
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if (2 * el <= r + no_eras - 1) {
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el = r + no_eras - el;
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/*
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* 2 lines below: B(x) <-- inv(discr_r) *
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* lambda(x)
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*/
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for (i = 0; i <= NROOTS; i++)
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b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
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} else {
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/* 2 lines below: B(x) <-- x*B(x) */
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memmove(&b[1],b,NROOTS*sizeof(b[0]));
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b[0] = A0;
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}
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memcpy(lambda,t,(NROOTS+1)*sizeof(t[0]));
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}
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}
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/* Convert lambda to index form and compute deg(lambda(x)) */
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deg_lambda = 0;
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for(i=0;i<NROOTS+1;i++){
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lambda[i] = INDEX_OF[lambda[i]];
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if(lambda[i] != A0)
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deg_lambda = i;
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}
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/* Find roots of the error+erasure locator polynomial by Chien search */
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memcpy(®[1],&lambda[1],NROOTS*sizeof(reg[0]));
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count = 0; /* Number of roots of lambda(x) */
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for (i = 1,k=IPRIM-1; i <= NN; i++,k = MODNN(k+IPRIM)) {
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q = 1; /* lambda[0] is always 0 */
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for (j = deg_lambda; j > 0; j--){
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if (reg[j] != A0) {
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reg[j] = MODNN(reg[j] + j);
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q ^= ALPHA_TO[reg[j]];
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}
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}
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if (q != 0)
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continue; /* Not a root */
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/* store root (index-form) and error location number */
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#if DEBUG>=2
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printf("count %d root %d loc %d\n",count,i,k);
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#endif
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root[count] = i;
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loc[count] = k;
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/* If we've already found max possible roots,
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* abort the search to save time
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*/
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if(++count == deg_lambda)
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break;
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}
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if (deg_lambda != count) {
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/*
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* deg(lambda) unequal to number of roots => uncorrectable
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* error detected
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*/
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count = -1;
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goto finish;
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}
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/*
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* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
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* x**NROOTS). in index form. Also find deg(omega).
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*/
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deg_omega = deg_lambda-1;
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for (i = 0; i <= deg_omega;i++){
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tmp = 0;
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for(j=i;j >= 0; j--){
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if ((s[i - j] != A0) && (lambda[j] != A0))
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tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
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}
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omega[i] = INDEX_OF[tmp];
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}
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/*
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* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
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* inv(X(l))**(FCR-1) and den = lambda_pr(inv(X(l))) all in poly-form
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*/
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for (j = count-1; j >=0; j--) {
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num1 = 0;
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for (i = deg_omega; i >= 0; i--) {
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if (omega[i] != A0)
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num1 ^= ALPHA_TO[MODNN(omega[i] + i * root[j])];
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}
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num2 = ALPHA_TO[MODNN(root[j] * (FCR - 1) + NN)];
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den = 0;
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/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
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for (i = MIN(deg_lambda,NROOTS-1) & ~1; i >= 0; i -=2) {
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if(lambda[i+1] != A0)
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den ^= ALPHA_TO[MODNN(lambda[i+1] + i * root[j])];
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}
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#if DEBUG >= 1
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if (den == 0) {
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printf("\n ERROR: denominator = 0\n");
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count = -1;
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goto finish;
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}
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#endif
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/* Apply error to data */
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if (num1 != 0 && loc[j] >= PAD) {
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data[loc[j]-PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN - INDEX_OF[den])];
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}
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}
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finish:
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if(eras_pos != NULL){
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for(i=0;i<count;i++)
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eras_pos[i] = loc[i];
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}
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retval = count;
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}
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