please dont rip this site
/*
 * Reed-Solomon coding and decoding
 * Phil Karn (karn at ka9q.ampr.org) August 1997
 * 
 * This file is derived from the program "new_rs_erasures.c" by Robert
 * Morelos-Zaragoza (robert at spectra.eng.hawaii.edu) and Hari Thirumoorthy
 * (harit at spectra.eng.hawaii.edu), Aug 1995
 *
 * This version is hard-wired to encode and decode the (255,223) code
 * over GF(256). It contains calls to i386 assembler routines optimized
 * for the Pentium.
 */
#include <stdio.h>
#include "rs32.h"

/* Primitive polynomials - see Lin & Costello, Error Control Coding Appendix A,
 * and  Lee & Messerschmitt, Digital Communication p. 453.
 */

/* 1+x^2+x^3+x^4+x^8 */
int Pp[MM+1] = { 1, 0, 1, 1, 1, 0, 0, 0, 1 };

/* Alpha exponent for the first root of the generator polynomial */
#define B0	1

/* index->polynomial form conversion table */
gf Alpha_to[NN + 1];

/* Polynomial->index form conversion table */
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)
 * Degree of g(x) = 2*TT
 * has roots @**B0, @**(B0+1), ... ,@^(B0+2*TT-1)
 */
gf Gg[NN - KK + 1];

/* Lookup table for multiplying by the 32 generator polynomial terms,
 * packed 4 terms to each 32-bit word
 */
unsigned long Gtab[8][256];

/* Lookup table for GF multiplication
 * Mtab[i][j] = j * alpha^(B0+i) (note limited range of i)
 */
unsigned char Mtab[NN-KK+1][NN+1];

/* 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];\
	}


/* generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[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] = Alpha_to[B0];
	Gg[1] = 1;		/* g(x) = (X+@**B0) initially */
	for (i = 2; i <= NN - KK; i++) {
		Gg[i] = 1;
		/*
		 * Below multiply (Gg[0]+Gg[1]*x + ... +Gg[i]x^i) by
		 * (@**(B0+i-1) + x)
		 */
		for (j = i - 1; j > 0; j--)
			if (Gg[j] != 0)
				Gg[j] = Gg[j - 1] ^ Alpha_to[modnn((Index_of[Gg[j]]) + B0 + i - 1)];
			else
				Gg[j] = Gg[j - 1];
		/* Gg[0] can never be zero */
		Gg[0] = Alpha_to[modnn((Index_of[Gg[0]]) + B0 + i - 1)];
	}
	/* convert Gg[] to index form for quicker encoding */
	for (i = 0; i <= NN - KK; i++)
		Gg[i] = Index_of[Gg[i]];
}


/* Generate lookup table for fast encoding
 * Each table entry contains four packed result per 32-bit word
 */
static void
gen_gtab(void)
{
	int i,ii,j,k,val;

	memset(Gtab,0,sizeof(Gtab));
	for(i=1;i<256;i++){
		ii = Index_of[i];
		for(j=0;j<8;j++){
			for(k=3;k>=0;k--){
				val = (Gg[4*j+k] == A0) ? 0 : Alpha_to[modnn(ii+Gg[4*j+k])];
				Gtab[j][i] = (Gtab[j][i] << 8) | val;
			}
		}
	}
}

/* Generate lookup table for fast syndrome computation in the decoder
 * Given a field element x in polynomial form, the table generated here
 * when indexed as Mtab[i][x] gives x * alpha**(B0+i)
 */
static void
gen_mtab(void)
{
	int i,j;

	for(i=0;i<NN-KK;i++){
		Mtab[i][0] = 0;
		for(j=1;j<=NN;j++){
			Mtab[i][j] = Alpha_to[modnn(Index_of[j] + B0 + i)];
		}
	}
}
void
init_rs(void)
{
	generate_gf();
	gen_poly();
	gen_gtab();
	gen_mtab();
}

/* Errors + erasures decoding of (255,223) RS code */
int
rsd32(dtype data[NN], int eras_pos[NN-KK], int no_eras)
{
	int deg_lambda, el, deg_omega;
	int i, j, r;
	gf u,q,tmp,num1,num2,den,discr_r;
	gf lambda[NN-KK + 1], s[NN-KK + 1];	/* Err+Eras Locator poly
						 * and syndrome poly */
	gf b[NN-KK + 1], t[NN-KK + 1], omega[NN-KK + 1];
	gf root[NN-KK], reg[NN-KK + 1];
	int syn_error, count;
	unsigned char st[NN-KK];

/*#define noasm */
#ifdef noasm
	memset(st,0,sizeof(st));
	for(i=254;i>=0;i--)
		for(j=0;j<32;j++)
			st[j] = data[i] ^ Mtab[j][st[j]];
#else
	rssyndrome(data,st);
#endif
	/* Convert syndromes to index form, checking for nonzero condition */
	syn_error = 0;
	for(i=0;i<NN-KK;i++){
		syn_error |= st[i];
		s[i+1] = Index_of[st[i]];
	}
	if (!syn_error) {
		/*
		 * if syndrome is zero, data[] is a codeword and there are no
		 * errors to correct. So return data[] unmodified
		 */
		return 0;
	}
	/* Check for and quickly correct the special case of a single error.
	 * This is indicated by
	 * s[i] / s[i+1] = @^-k for all i and some constant k,
	 *	 (s in polynomial form), or
	 * s[i] - s[i+1] = -k,
	 *	 (s in index form)
	 *
	 * See Clark & Cain, "Error Correction Coding for Digital
	 * Communications", p209-210.
	 */
	if(s[2] != A0 && s[1] != A0){
		tmp = modnn(s[2] - s[1] + NN);	/* s[] in index form */
		for(i=2;i<NN-KK;i++){
			if(s[i+1] == A0 || s[i] == A0
			 || modnn(s[i+1] - s[i] + NN) != tmp)
			break;
		}
		if(i == NN-KK){
			/* single error */
			data[tmp] ^= Alpha_to[modnn(s[1] - tmp + NN)];
			return 1;
		}
	}
	CLEAR(&lambda[1],NN-KK);
	lambda[0] = 1;
	if (no_eras > 0) {
		/* Init lambda to be the erasure locator polynomial */
		lambda[1] = Alpha_to[eras_pos[0]];
		for (i = 1; i < no_eras; i++) {
			u = 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)];
			}
		}
	}
	for(i=0;i<NN-KK+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 <= NN-KK) {	/* 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] != A0)) {
				discr_r ^= Alpha_to[modnn(Index_of[lambda[i]] + s[r - i])];
			}
		}
		discr_r = Index_of[discr_r];	/* Index form */
		if (discr_r == A0) {
			/* 2 lines below: B(x) <-- x*B(x) */
			COPYDOWN(&b[1],b,NN-KK);
			b[0] = A0;
		} else {
			/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
			t[0] = lambda[0];
			for (i = 0 ; i < NN-KK; 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 <= NN-KK; i++)
					b[i] = (lambda[i] == 0) ? A0 : modnn(Index_of[lambda[i]] - discr_r + NN);
			} else {
				/* 2 lines below: B(x) <-- x*B(x) */
				COPYDOWN(&b[1],b,NN-KK);
				b[0] = A0;
			}
			COPY(lambda,t,NN-KK+1);
		}
	}

	/* Convert lambda to index form and compute deg(lambda(x)) */
	deg_lambda = 0;
	for(i=0;i<NN-KK+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
	 */
	COPY(&reg[1],&lambda[1],NN-KK);
	count = 0;		/* Number of roots of lambda(x) */
	for (i = 1; i <= NN; i++) {
		q = 1;
		for (j = deg_lambda; j > 0; j--)
			if (reg[j] != A0) {
				reg[j] = modnn(reg[j] + j);
				q ^= Alpha_to[reg[j]];
			}
		if (!q) {
			/* store root (index-form) and error location number */
			root[count++] = i;
			if(count == deg_lambda)
				/* Found all possible roots, no point in continuing */
				break;
		}
	}

#ifdef DEBUG
	printf("\n Final error positions:\t");
	for (i = 0; i < count; i++)
		printf("%d ", NN - root[i]);
	printf("\n");
#endif
	if (deg_lambda != count) {
		/*
		 * deg(lambda) unequal to number of roots => uncorrectable
		 * error detected
		 */
		return -1;
	}
	/*
	 * Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
	 * x**(NN-KK)). in index form. Also find deg(omega).
	 */
	deg_omega = 0;
	for (i = 0; i < NN-KK;i++){
		tmp = 0;
		j = (deg_lambda < i) ? deg_lambda : i;
		for(;j >= 0; j--){
			if ((s[i + 1 - j] != A0) && (lambda[j] != A0))
				tmp ^= Alpha_to[modnn(s[i + 1 - j] + lambda[j])];
		}
		if(tmp != 0)
			deg_omega = i;
		omega[i] = Index_of[tmp];
	}
	omega[NN-KK] = A0;

	/*
	 * Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
	 * inv(X(l))**(B0-1) 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] * (B0 - 1) + NN)];
		den = 0;

		/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
		for (i = min(deg_lambda,NN-KK-1) & ~1; i >= 0; i -=2) {
			if(lambda[i+1] != A0)
				den ^= Alpha_to[modnn(lambda[i+1] + i * root[j])];
		}
		if (den == 0) {
#ifdef DEBUG
			printf("\n ERROR: denominator = 0\n");
#endif
			return -1;
		}
		/* Apply error to data */
		if (num1 != 0) {
			data[NN - root[j]] ^= Alpha_to[modnn(Index_of[num1] + Index_of[num2] + NN - Index_of[den])];
		}
	}
	return count;
}

file: /Techref/method/error/rs-255-223-3-pf-qc-1999/rs32_c.htm, 75KB, , updated: 2000/5/10 12:20, local time: 2024/11/22 10:28,
TOP NEW HELP FIND: 
18.116.81.255:LOG IN

 ©2024 These pages are served without commercial sponsorship. (No popup ads, etc...).Bandwidth abuse increases hosting cost forcing sponsorship or shutdown. This server aggressively defends against automated copying for any reason including offline viewing, duplication, etc... Please respect this requirement and DO NOT RIP THIS SITE. Questions?
Please DO link to this page! Digg it! / MAKE!

<A HREF="http://ecomorder.com/techref/method/error/rs-255-223-3-pf-qc-1999/rs32_c.htm"> Colorized Source Code</A>

After you find an appropriate page, you are invited to your to this massmind site! (posts will be visible only to you before review) Just type a nice message (short messages are blocked as spam) in the box and press the Post button. (HTML welcomed, but not the <A tag: Instead, use the link box to link to another page. A tutorial is available Members can login to post directly, become page editors, and be credited for their posts.


Link? Put it here: 
if you want a response, please enter your email address: 
Attn spammers: All posts are reviewed before being made visible to anyone other than the poster.
Did you find what you needed?

 

Welcome to ecomorder.com!

 

Welcome to ecomorder.com!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  .