前向纠错的多个算法C语言

/* * Reed-Solomon coding and decoding * Phil Karn (karn@ka9q.ampr.org) September 1996 * Separate CCSDS version create Dec 1998, merged into this version May 1999 * * This file is derived from my generic RS encoder/decoder, which is * in turn based on the program "new_rs_erasures.c" by Robert * Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari Thirumoorthy * (harit@spectra.eng.hawaii.edu), Aug 1995 * Copyright 1999 Phil Karn, KA9Q * May be used under the terms of the GNU public license */ #include <stdio.h> #include "rs.h" #ifdef CCSDS /* CCSDS field generator polynomial: 1+x+x^2+x^7+x^8 */ int Pp[MM+1] = { 1, 1, 1, 0, 0, 0, 0, 1, 1 }; #else /* not CCSDS */ /* MM, KK, B0, PRIM are user-defined in rs.h */ /* Primitive polynomials - see Lin & Costello, Appendix A, * and Lee & Messerschmitt, p. 453. */ #if(MM == 2)/* Admittedly silly */ int Pp[MM+1] = { 1, 1, 1 }; #elif(MM == 3) /* 1 + x + x^3 */ int Pp[MM+1] = { 1, 1, 0, 1 }; #elif(MM == 4) /* 1 + x + x^4 */ int Pp[MM+1] = { 1, 1, 0, 0, 1 }; #elif(MM == 5) /* 1 + x^2 + x^5 */ int Pp[MM+1] = { 1, 0, 1, 0, 0, 1 }; #elif(MM == 6) /* 1 + x + x^6 */ int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1 }; #elif(MM == 7) /* 1 + x^3 + x^7 */ int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 1 }; #elif(MM == 8) /* 1+x^2+x^3+x^4+x^8 */ int Pp[MM+1] = { 1, 0, 1, 1, 1, 0, 0, 0, 1 }; #elif(MM == 9) /* 1+x^4+x^9 */ int Pp[MM+1] = { 1, 0, 0, 0, 1, 0, 0, 0, 0, 1 }; #elif(MM == 10) /* 1+x^3+x^10 */ int Pp[MM+1] = { 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 }; #elif(MM == 11) /* 1+x^2+x^11 */ int Pp[MM+1] = { 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; #elif(MM == 12) /* 1+x+x^4+x^6+x^12 */ int Pp[MM+1] = { 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1 }; #elif(MM == 13) /* 1+x+x^3+x^4+x^13 */ int Pp[MM+1] = { 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; #elif(MM == 14) /* 1+x+x^6+x^10+x^14 */ int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 }; #elif(MM == 15) /* 1+x+x^15 */ int Pp[MM+1] = { 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 }; #elif(MM == 16) /* 1+x+x^3+x^12+x^16 */ int Pp[MM+1] = { 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 }; #else #error "Either CCSDS must be defined, or MM must be set in range 2-16" #endif #endif /* This defines the type used to store an element of the Galois Field * used by the code. Make sure this is something larger than a char if * if anything larger than GF(256) is used. * * Note: unsigned char will work up to GF(256) but int seems to run * faster on the Pentium. */ typedef int gf; /* index->polynomial form conversion table */ static gf Alpha_to[NN + 1]; /* Polynomial->index form conversion table */ static gf Index_of[NN + 1]; /* No legal value in index form represents zero, so * we need a special value for this purpose */ #define A0 (NN) /* Generator polynomial g(x) in index form */ static gf Gg[NN - KK + 1]; static int RS_init; /* Initialization flag */ /* Compute x % NN, where NN is 2**MM - 1, * without a slow divide */ static inline gf modnn(int x) { while (x >= NN) { x -= NN; x = (x >> MM) + (x & NN); } return x; } #define min(a,b) ((a) < (b) ? (a) : (b)) #define CLEAR(a,n) {\ int ci;\ for(ci=(n)-1;ci >=0;ci--)\ (a)[ci] = 0;\ } #define COPY(a,b,n) {\ int ci;\ for(ci=(n)-1;ci >=0;ci--)\ (a)[ci] = (b)[ci];\ } #define COPYDOWN(a,b,n) {\ int ci;\ for(ci=(n)-1;ci >=0;ci--)\ (a)[ci] = (b)[ci];\ } static void init_rs(void); #ifdef CCSDS /* Conversion lookup tables from conventional alpha to Berlekamp's * dual-basis representation. Used in the CCSDS version only. * taltab[] -- convert conventional to dual basis * tal1tab[] -- convert dual basis to conventional * Note: the actual RS encoder/decoder works with the conventional basis. * So data is converted from dual to conventional basis before either * encoding or decoding and then converted back. */ static unsigned char taltab[NN+1],tal1tab[NN+1]; static unsigned char tal[] = { 0x8d, 0xef, 0xec, 0x86, 0xfa, 0x99, 0xaf, 0x7b }; /* Generate conversion lookup tables between conventional alpha representation * (@**7, @**6, ...@**0) * and Berlekamp's dual basis representation * (l0, l1, ...l7) */ static void gen_ltab(void) { int i,j,k; for(i=0;i<256;i++){/* For each value of input */ taltab[i] = 0; for(j=0;j<8;j++) /* for each column of matrix */ for(k=0;k<8;k++){ /* for each row of matrix */ if(i & (1<<k)) taltab[i] ^= tal[7-k] & (1<<j); } tal1tab[taltab[i]] = i; } } #endif /* CCSDS */ #if PRIM != 1 static int Ldec;/* Decrement for aux location variable in Chien search */ static void gen_ldec(void) { for(Ldec=1;(Ldec % PRIM) != 0;Ldec+= NN) ; Ldec /= PRIM; } #else #define Ldec 1 #endif /* generate GF(2**m) from the irreducible polynomial p(X) in Pp[0]..Pp[m] lookup tables: index->polynomial form alpha_to[] contains j=alpha**i; polynomial form -> index form index_of[j=alpha**i] = i alpha=2 is the primitive element of GF(2**m) HARI's COMMENT: (4/13/94) alpha_to[] can be used as follows: Let @ represent the primitive element commonly called "alpha" that is the root of the primitive polynomial p(x). Then in GF(2^m), for any 0 <= i <= 2^m-2, @^i = a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1) where the binary vector (a(0),a(1),a(2),...,a(m-1)) is the representation of the integer "alpha_to[i]" with a(0) being the LSB and a(m-1) the MSB. Thus for example the polynomial representation of @^5 would be given by the binary representation of the integer "alpha_to[5]". Similarily, index_of[] can be used as follows: As above, let @ represent the primitive element of GF(2^m) that is the root of the primitive polynomial p(x). In order to find the power of @ (alpha) that has the polynomial representation a(0) + a(1) @ + a(2) @^2 + ... + a(m-1) @^(m-1) we consider the integer "i" whose binary representation with a(0) being LSB and a(m-1) MSB is (a(0),a(1),...,a(m-1)) and locate the entry "index_of[i]". Now, @^index_of[i] is that element whose polynomial representation is (a(0),a(1),a(2),...,a(m-1)). NOTE: The element alpha_to[2^m-1] = 0 always signifying that the representation of "@^infinity" = 0 is (0,0,0,...,0). Similarily, the element index_of[0] = A0 always signifying that the power of alpha which has the polynomial representation (0,0,...,0) is "infinity". */ static void generate_gf(void) { register int i, mask; mask = 1; Alpha_to[MM] = 0; for (i = 0; i < MM; i++) { Alpha_to[i] = mask; Index_of[Alpha_to[i]] = i; /* If Pp[i] == 1 then, term @^i occurs in poly-repr of @^MM */ if (Pp[i] != 0) Alpha_to[MM] ^= mask; /* Bit-wise EXOR operation */ mask <<= 1; /* single left-shift */ } Index_of[Alpha_to[MM]] = MM; /* * Have obtained poly-repr of @^MM. Poly-repr of @^(i+1) is given by * poly-repr of @^i shifted left one-bit and accounting for any @^MM * term that may occur when poly-repr of @^i is shifted. */ mask >>= 1; for (i = MM + 1; i < NN; i++) { if (Alpha_to[i - 1] >= mask) Alpha_to[i] = Alpha_to[MM] ^ ((Alpha_to[i - 1] ^ mask) << 1); else Alpha_to[i] = Alpha_to[i - 1] << 1; Index_of[Alpha_to[i]] = i; } Index_of[0] = A0; Alpha_to[NN] = 0; } /* * Obtain the generator polynomial of the TT-error correcting, length * NN=(2**MM -1) Reed Solomon code from the product of (X+@**(B0+i)), i = 0, * ... ,(2*TT-1) * * Examples: * * If B0 = 1, TT = 1. deg(g(x)) = 2*TT = 2. * g(x) = (x+@) (x+@**2) * * If B0 = 0, TT = 2. deg(g(x)) = 2*TT = 4. * g(x) = (x+1) (x+@) (x+@**2) (x+@**3) */ static void gen_poly(void) { register int i, j;