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package org.yamcs.rs;
/* Reed-Solomon decoder
* Copyright 2002 Phil Karn, KA9Q
* May be used under the terms of the GNU Lesser General Public License (LGPL)
*
* Translated from C to Java by Nicolae Mihalache, Space Applications Services
*/
import java.util.Arrays;
/**
* Reed-Solomon encoder/decoder.
*
*/
public class ReedSolomon {
int nroots;
final int nn;
final byte[] _alpha_to;
final byte[] _index_of;
final int fcr;
final int prim;
int iprim;
// Special reserved value encoding zero in index form
byte A0;
int gfpoly;
int symsize;
final byte[] genpoly;
final int pad;
/**
* Constructs a new encoder/decoder.
*
* @param nroots
* the number of roots in the Reed Solomon code generator polynomial. This equals the number of parity
* symbols per code block.
* @param symsize
* the symbol size in bits, up to 8
* @param fcr
* in index form, the first consecutive root of the Reed Solomon code generator polynomial.
* @param prim
* in index form, the primitive element in the Galois field used to generate the Reed Solomon code
* generator polynomial.
* @param gfpoly
* the extended Galois field generator polynomial coefficients, with the 0th coefficient in the low order
* bit. The polynomial must be primitive; if not, an IllegalArgumentException will be thrown.
*
* @param pad
* the number of leading symbols in the codeword that are implicitly padded to zero in a shortened code
* block
*/
public ReedSolomon(int nroots, int symsize, int fcr, int prim, int gfpoly, int pad) {
if (symsize < 2 || symsize > 8) {
throw new IllegalArgumentException("Invalid symbol size");
}
this.nn = (1 << symsize) - 1;
if (fcr < 0 || fcr > nn) {
throw new IllegalArgumentException("Invalid fcr");
}
if (prim <= 0 || prim > nn) {
throw new IllegalArgumentException("Invalid prim");
}
if (nroots < 0 || nroots > nn) {
throw new IllegalArgumentException("Can't have more roots than symbol values!");
}
if (pad < 0 || pad >= (nn - nroots)) {
throw new IllegalArgumentException("Too much padding");
}
this.nroots = nroots;
this.symsize = symsize;
this._alpha_to = new byte[nn + 1];
this._index_of = new byte[nn + 1];
this.fcr = fcr;
this.prim = prim;
this.A0 = (byte) nn;
this.gfpoly = gfpoly;
this.genpoly = new byte[nroots + 1];
this.pad = pad;
init();
}
private void init() {
_index_of[0] = A0;
_alpha_to[A0 & 0xFF] = 0;
int sr = 1;
for (int i = 0; i < nn; i++) {
_index_of[sr] = (byte) i;
_alpha_to[i] = (byte) sr;
sr <<= 1;
if ((sr & (1 << symsize)) != 0) {
sr ^= gfpoly;
}
sr &= nn;
}
if (sr != 1) {
throw new IllegalArgumentException("field generator polynomial is not primitive!");
}
/* Find prim-th root of 1, used in decoding */
for (iprim = 1; (iprim % prim) != 0; iprim += nn)
;
iprim = iprim / prim;
genpoly[0] = 1;
for (int i = 0, root = fcr * prim; i < nroots; i++, root += prim) {
genpoly[i + 1] = 1;
/* Multiply rs->genpoly[] by @**(root + x) */
for (int j = i; j > 0; j--) {
if (genpoly[j] != 0)
genpoly[j] = (byte) (genpoly[j - 1] ^ alpha_to(index_of(genpoly[j]), root));
else
genpoly[j] = genpoly[j - 1];
}
/* rs->genpoly[0] can never be zero */
genpoly[0] = alpha_to(index_of(genpoly[0]), root);
}
/* convert rs->genpoly[] to index form for quicker encoding */
for (int i = 0; i <= nroots; i++) {
genpoly[i] = index_of(genpoly[i]);
}
}
/**
* Generate the parity for the given data
*
* @param data
* - data to be encoded
* @param parity
* - the resulting parity bytes
*/
public void encode(byte[] data, byte[] parity) {
int i, j;
byte feedback;
Arrays.fill(parity, (byte) 0);
for (i = 0; i < nn - nroots - pad; i++) {
feedback = index_of(data[i] ^ parity[0]);
if (feedback != A0) { /* feedback term is non-zero */
for (j = 1; j < nroots; j++) {
parity[j] ^= alpha_to(feedback, genpoly[nroots - j]);
}
}
/* Shift */
System.arraycopy(parity, 1, parity, 0, nroots - 1);
if (feedback != A0) {
parity[nroots - 1] = alpha_to(feedback, genpoly[0]);
} else {
parity[nroots - 1] = 0;
}
}
}
/**
* Corrects in place data and returns the number of error corrected.
*
* @param data
* - data to be corrected
* @param eras_pos
* - erasures positions (can be null)
* @return
* @throws ReedSolomonException
* - thrown if the data cannot be corrected
*/
public int decode(byte[] data, int[] eras_pos) throws ReedSolomonException {
int deg_lambda, el, deg_omega;
int i, j, r, k;
byte u, q, tmp, num1, num2, den, discr_r;
byte[] lambda = new byte[nroots + 1];
byte[] s = new byte[nroots]; /*
* Err+Eras Locator poly
* and syndrome poly
*/
byte[] b = new byte[nroots + 1];
byte[] t = new byte[nroots + 1];
byte[] omega = new byte[nroots + 1];
int[] root = new int[nroots];
byte[] reg = new byte[nroots + 1];
int[] loc = new int[nroots];
int syn_error, count;
for (i = 0; i < nroots; i++) {
s[i] = data[0];
}
/* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
for (j = 1; j < nn - pad; j++) {
for (i = 0; i < nroots; i++) {
if (s[i] == 0) {
s[i] = data[j];
} else {
s[i] = (byte) (data[j] ^ alpha_to(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 == 0) {
/*
* if syndrome is zero, data[] is a codeword and there are no
* errors to correct. So return data[] unmodified
*/
count = 0;
return 0;
}
lambda[0] = 1;
int no_eras = 0;
if (eras_pos != null) {
no_eras = eras_pos.length;
/* Init lambda to be the erasure locator polynomial */
lambda[1] = alpha_to(prim * (nn - 1 - eras_pos[0]));
for (i = 1; i < eras_pos.length; i++) {
u = (byte) 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(u, tmp);
}
}
}
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(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]));
System.arraycopy(b, 0, b, 1, nroots);
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] = (byte) (lambda[i + 1] ^ alpha_to(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] = (byte) ((lambda[i] == 0) ? A0
: modnn((0xFF & index_of(lambda[i])) - (0xFF & discr_r) + nn));
}
} else {
/* 2 lines below: B(x) <-- x*B(x) */
// memmove(&b[1],b,NROOTS*sizeof(b[0]));
System.arraycopy(b, 0, b, 1, nroots);
b[0] = A0;
}
// memcpy(lambda,t,(NROOTS+1)*sizeof(t[0]));
System.arraycopy(t, 0, lambda, 0, nroots + 1);
}
}
/* 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(®[1],&lambda[1],NROOTS*sizeof(reg[0]));
System.arraycopy(lambda, 1, reg, 1, nroots);
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] = (byte) modnn((0xFF & reg[j]) + j);
q ^= alpha_to(reg[j]);
}
}
if (q != 0)
continue; /* Not a root */
/* store root (index-form) and error location number */
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;
throw new ReedSolomonException("Uncorrectable");
}
/*
* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
* x**NROOTS). in index form. Also find deg(omega).
*/
deg_omega = deg_lambda - 1;
for (i = 0; i <= deg_omega; i++) {
tmp = 0;
for (j = i; j >= 0; j--) {
if ((s[i - j] != A0) && (lambda[j] != A0))
tmp ^= alpha_to(s[i - j], lambda[j]);
}
omega[i] = index_of(tmp);
}
/*
* 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(omega[i], i * root[j]);
}
num2 = alpha_to(root[j] * (fcr - 1) + nn);
den = 0;
/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
for (i = Integer.min(deg_lambda, nroots - 1) & ~1; i >= 0; i -= 2) {
if (lambda[i + 1] != A0)
den ^= alpha_to(lambda[i + 1], i * root[j]);
}
/* Apply error to data */
if (num1 != 0 && loc[j] >= pad) {
data[loc[j] - pad] ^= alpha_to(
(index_of(num1) & 0xFF) + (index_of(num2) & 0xFF) + nn - (index_of(den) & 0xFF));
}
}
if (eras_pos != null) {
for (i = 0; i < count; i++)
eras_pos[i] = loc[i];
}
return count;
}
private byte index_of(int x) {
return _index_of[x & 0xFF];
}
private byte alpha_to(int x) {
while (x >= nn) {
x -= nn;
}
return _alpha_to[x];
}
private byte alpha_to(byte x) {
return _alpha_to[x & 0xFF];
}
private byte alpha_to(byte x, int y) {
return alpha_to(y + (x & 0xFF));
}
private byte alpha_to(byte x, byte y) {
return alpha_to((x & 0xFF) + (y & 0xFF));
}
private int modnn(int x) {
while (x >= nn) {
x -= nn;
}
return x;
}
public int nroots() {
return nroots;
}
public int blockSize() {
return nn;
}
}
