RS码编译码程序，c语言编写

/* Reed-Solomon decoder * Copyright 2002 Phil Karn, KA9Q * May be used under the terms of the GNU General Public License (GPL) */ #ifdef DEBUG #include <stdio.h> #endif #include <string.h> #define NULL ((void *)0) #define min(a,b) ((a) < (b) ? (a) : (b)) #ifdef FIXED #include "fixed.h" #elif defined(BIGSYM) #include "int.h" #else #include "char.h" #endif int DECODE_RS( #ifndef FIXED void *p, #endif DTYPE *data, int *eras_pos, int no_eras){ #ifndef FIXED struct rs *rs = (struct rs *)p; #endif int deg_lambda, el, deg_omega; int i, j, r,k; DTYPE u,q,tmp,num1,num2,den,discr_r; DTYPE lambda[NROOTS+1], s[NROOTS]; /* Err+Eras Locator poly * and syndrome poly */ DTYPE b[NROOTS+1], t[NROOTS+1], omega[NROOTS+1]; DTYPE 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;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 = 0; for (i = 0; i < NROOTS;i++){ tmp = 0; j = (deg_lambda < i) ? deg_lambda : i; for(;j >= 0; j--){ if ((s[i - j] != A0) && (lambda[j] != A0)) tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])]; } if(tmp != 0) deg_omega = i; omega[i] = INDEX_OF[tmp]; } omega[NROOTS] = A0; /* * 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 (den == 0) { #if DEBUG >= 1 printf("\n ERROR: denominator = 0\n"); #endif count = -1; goto finish; } /* Apply error to data */ if (num1 != 0) { data[loc[j]] ^= 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]; } return count; }