rs.c

Reed-Solomn code 编译码(含CCSDS鞋译） 算法

/*
 * Reed-Solomon coding and decoding
 * Phil Karn ([e-mail]) 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 ([e-mail]) and Hari Thirumoorthy
 * ([e-mail]), 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;

  Gg[0] = 1;
  for (i = 0; i < NN - KK; i++) {
    Gg[i+1] = 1;
    /*
     * Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
     * (@**(B0+i)*PRIM + x)
     */
    for (j = i; j > 0; j--)
      if (Gg[j] != 0)
	Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + (B0 + i) *PRIM)];
      else
	Gg[j] = Gg[j - 1];
    /* Gg[0] can never be zero */
    Gg[0] = Alpha_to[modnn(Index_of[Gg[0]] + (B0 + i) * PRIM)];
  }
  /* convert Gg[] to index form for quicker encoding */
  for (i = 0; i <= NN - KK; i++)
    Gg[i] = Index_of[Gg[i]];
}


/*
 * take the string of symbols in data[i], i=0..(k-1) and encode
 * systematically to produce NN-KK parity symbols in bb[0]..bb[NN-KK-1] data[]
 * is input and bb[] is output in polynomial form. Encoding is done by using
 * a feedback shift register with appropriate connections specified by the
 * elements of Gg[], which was generated above. Codeword is   c(X) =
 * data(X)*X**(NN-KK)+ b(X)
 */
int
encode_rs(dtype data[KK], dtype bb[NN-KK])
{
  register int i, j;
  gf feedback;

#if DEBUG >= 1 && MM != 8
  /* Check for illegal input values */
  for(i=0;i<KK;i++)
    if(data[i] > NN)
      return -1;
#endif