www.pudn.com > QRcode.rar > ReedSolomon.java
/*
* このクラスファイル「ReedSolomon.java」は、Henry Minsky氏が
* 作成したプログラム「RSCODE」をの一部をJava向けに改変したものです。
* 関連情報： https://sourceforge.net/projects/rscode/
*/
package jp.sourceforge.qrcode.codec.ecc;
public class ReedSolomon {
//G(x)=α^8+α^4+α^3+α^2+1
int[] y;
int[] gexp = new int[512];
int[] glog = new int[256];
final int NPAR = 4;
final int MAXDEG = NPAR*2;
int[] synBytes = new int[MAXDEG];
/* The Error Locator Polynomial, also known as Lambda or Sigma. Lambda[0] == 1 */
int[] Lambda = new int[MAXDEG];
/* The Error Evaluator Polynomial */
int[] Omega = new int[MAXDEG];
/* local ANSI declarations */
/* error locations found using Chien's search*/
int[] ErrorLocs = new int[256];
int NErrors;
/* erasure flags */
int[] ErasureLocs = new int[256];
int NErasures = 0;
void initializeGaloisTables() {
int i, z;
int pinit,p1,p2,p3,p4,p5,p6,p7,p8;
pinit = p2 = p3 = p4 = p5 = p6 = p7 = p8 = 0;
p1 = 1;
gexp[0] = 1;
gexp[255] = gexp[0];
glog[0] = 0; /* shouldn't log[0] be an error? */
for (i = 1; i < 256; i++) {
pinit = p8;
p8 = p7;
p7 = p6;
p6 = p5;
p5 = p4 ^ pinit;
p4 = p3 ^ pinit;
p3 = p2 ^ pinit;
p2 = p1;
p1 = pinit;
gexp[i] = p1 + p2*2 + p3*4 + p4*8 + p5*16 + p6*32 + p7*64 + p8*128;
gexp[i+255] = gexp[i];
}
for (i = 1; i < 256; i++) {
for (z = 0; z < 256; z++) {
if (gexp[z] == i) {
glog[i] = z;
break;
}
}
}
}
/* multiplication using logarithms */
int gmult(int a, int b)
{
int i,j;
if (a==0 || b == 0) return (0);
i = glog[a];
j = glog[b];
return (gexp[i+j]);
}
int ginv (int elt)
{
return (gexp[255-glog[elt]]);
}
public ReedSolomon(int[] source) {
initializeGaloisTables();
y = source;
}
void decode_data(int[] data)
{
int i, j, sum;
for (j = 0; j < 8; j++) {
sum = 0;
for (i = 0; i < data.length; i++) {
sum = data[i] ^ gmult(gexp[j+1], sum);
}
synBytes[j] = sum;
}
}
public void correct() {
// return;
decode_data(y);
boolean hasError = false;
for (int i = 0; i < synBytes.length; i++) {
//System.out.println("SyndromeS"+String.valueOf(i) + " = " + synBytes[i]);
if (synBytes[i] != 0)
hasError = true;
}
if (hasError)
correct_errors_erasures (y, y.length, 0, new int[1]);
}
public int getNumCorrectedErrors() {
return NErrors;
}
/* From Cain, Clark, "Error-Correction Coding For Digital Communications", pp. 216. */
void
Modified_Berlekamp_Massey ()
{
int n, L, L2, k, d, i;
int[] psi = new int[MAXDEG];
int[] psi2 = new int[MAXDEG];
int[] D = new int[MAXDEG];
int[] gamma = new int[MAXDEG];
/* initialize Gamma, the erasure locator polynomial */
init_gamma(gamma);
/* initialize to z */
copy_poly(D, gamma);
mul_z_poly(D);
copy_poly(psi, gamma);
k = -1; L = NErasures;
for (n = NErasures; n < 8; n++) {
d = compute_discrepancy(psi, synBytes, L, n);
if (d != 0) {
/* psi2 = psi - d*D */
for (i = 0; i < MAXDEG; i++) psi2[i] = psi[i] ^ gmult(d, D[i]);
if (L < (n-k)) {
L2 = n-k;
k = n-L;
/* D = scale_poly(ginv(d), psi); */
for (i = 0; i < MAXDEG; i++) D[i] = gmult(psi[i], ginv(d));
L = L2;
}
/* psi = psi2 */
for (i = 0; i < MAXDEG; i++) psi[i] = psi2[i];
}
mul_z_poly(D);
}
for(i = 0; i < MAXDEG; i++) Lambda[i] = psi[i];
compute_modified_omega();
}
/* given Psi (called Lambda in Modified_Berlekamp_Massey) and synBytes,
compute the combined erasure/error evaluator polynomial as
Psi*S mod z^4
*/
void
compute_modified_omega ()
{
int i;
int[] product = new int[MAXDEG*2];
mult_polys(product, Lambda, synBytes);
zero_poly(Omega);
for(i = 0; i < NPAR; i++) Omega[i] = product[i];
}
/* polynomial multiplication */
void
mult_polys (int[] dst, int[] p1, int[] p2)
{
int i, j;
int[] tmp1 = new int[MAXDEG*2];
for (i=0; i < (MAXDEG*2); i++) dst[i] = 0;
for (i = 0; i < MAXDEG; i++) {
for(j=MAXDEG; j<(MAXDEG*2); j++) tmp1[j]=0;
/* scale tmp1 by p1[i] */
for(j=0; j= i; j--) tmp1[j] = tmp1[j-i];
for (j = 0; j < i; j++) tmp1[j] = 0;
/* add into partial product */
for(j=0; j < (MAXDEG*2); j++) dst[j] ^= tmp1[j];
}
}
/* gamma = product (1-z*a^Ij) for erasure locs Ij */
void
init_gamma (int[] gamma)
{
int e;
int[] tmp = new int[MAXDEG];
zero_poly(gamma);
zero_poly(tmp);
gamma[0] = 1;
for (e = 0; e < NErasures; e++) {
copy_poly(tmp, gamma);
scale_poly(gexp[ErasureLocs[e]], tmp);
mul_z_poly(tmp);
add_polys(gamma, tmp);
}
}
void
compute_next_omega (int d, int[] A, int[] dst, int[] src)
{
int i;
for ( i = 0; i < MAXDEG; i++) {
dst[i] = src[i] ^ gmult(d, A[i]);
}
}
int
compute_discrepancy (int[] lambda, int[] S, int L, int n)
{
int i, sum=0;
for (i = 0; i <= L; i++)
sum ^= gmult(lambda[i], S[n-i]);
return (sum);
}
/********** polynomial arithmetic *******************/
void add_polys (int[] dst, int[] src)
{
int i;
for (i = 0; i < MAXDEG; i++) dst[i] ^= src[i];
}
void copy_poly (int[] dst, int[] src)
{
int i;
for (i = 0; i < MAXDEG; i++) dst[i] = src[i];
}
void scale_poly (int k, int[] poly)
{
int i;
for (i = 0; i < MAXDEG; i++) poly[i] = gmult(k, poly[i]);
}
void zero_poly (int[] poly)
{
int i;
for (i = 0; i < MAXDEG; i++) poly[i] = 0;
}
/* multiply by z, i.e., shift right by 1 */
void mul_z_poly (int[] src)
{
int i;
for (i = MAXDEG-1; i > 0; i--) src[i] = src[i-1];
src[0] = 0;
}
/* Finds all the roots of an error-locator polynomial with coefficients
* Lambda[j] by evaluating Lambda at successive values of alpha.
*
* This can be tested with the decoder's equations case.
*/
void Find_Roots ()
{
int sum, r, k;
NErrors = 0;
for (r = 1; r < 256; r++) {
sum = 0;
/* evaluate lambda at r */
for (k = 0; k < NPAR+1; k++) {
sum ^= gmult(gexp[(k*r)%255], Lambda[k]);
}
if (sum == 0)
{
ErrorLocs[NErrors] = (255-r); NErrors++;
//if (DEBUG) fprintf(stderr, "Root found at r = %d, (255-r) = %d\n", r, (255-r));
}
}
}
/* Combined Erasure And Error Magnitude Computation
*
* Pass in the codeword, its size in bytes, as well as
* an array of any known erasure locations, along the number
* of these erasures.
*
* Evaluate Omega(actually Psi)/Lambda' at the roots
* alpha^(-i) for error locs i.
*
* Returns 1 if everything ok, or 0 if an out-of-bounds error is found
*
*/
int correct_errors_erasures (int[] codeword,
int csize,
int nerasures,
int[] erasures)
{
int r, i, j, err;
/* If you want to take advantage of erasure correction, be sure to
set NErasures and ErasureLocs[] with the locations of erasures.
*/
NErasures = nerasures;
for (i = 0; i < NErasures; i++) ErasureLocs[i] = erasures[i];
Modified_Berlekamp_Massey();
Find_Roots();
if ((NErrors <= NPAR) && NErrors > 0) {
/* first check for illegal error locs */
for (r = 0; r < NErrors; r++) {
if (ErrorLocs[r] >= csize) {
//if (DEBUG) fprintf(stderr, "Error loc i=%d outside of codeword length %d\n", i, csize);
return(0);
}
}
for (r = 0; r < NErrors; r++) {
int num, denom;
i = ErrorLocs[r];
/* evaluate Omega at alpha^(-i) */
num = 0;
for (j = 0; j < MAXDEG; j++)
num ^= gmult(Omega[j], gexp[((255-i)*j)%255]);
/* evaluate Lambda' (derivative) at alpha^(-i) ; all odd powers disappear */
denom = 0;
for (j = 1; j < MAXDEG; j += 2) {
denom ^= gmult(Lambda[j], gexp[((255-i)*(j-1)) % 255]);
}
err = gmult(num, ginv(denom));
//if (DEBUG) fprintf(stderr, "Error magnitude %#x at loc %d\n", err, csize-i);
codeword[csize-i-1] ^= err;
}
//for (int p = 0; p < codeword.length; p++)
// System.out.println(codeword[p]);
return(1);
}
else {
//if (DEBUG && NErrors) fprintf(stderr, "Uncorrectable codeword\n");
return(0);
}
}
}