ReedSolomonDecoder.java
/*
* Copyright 2007 ZXing authors
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.google.zxing.common.reedsolomon;
/**
* <p>Implements Reed-Solomon decoding, as the name implies.</p>
*
* <p>The algorithm will not be explained here, but the following references were helpful
* in creating this implementation:</p>
*
* <ul>
* <li>Bruce Maggs.
* <a href="http://www.cs.cmu.edu/afs/cs.cmu.edu/project/pscico-guyb/realworld/www/rs_decode.ps">
* "Decoding Reed-Solomon Codes"</a> (see discussion of Forney's Formula)</li>
* <li>J.I. Hall. <a href="www.mth.msu.edu/~jhall/classes/codenotes/GRS.pdf">
* "Chapter 5. Generalized Reed-Solomon Codes"</a>
* (see discussion of Euclidean algorithm)</li>
* </ul>
*
* <p>Much credit is due to William Rucklidge since portions of this code are an indirect
* port of his C++ Reed-Solomon implementation.</p>
*
* @author Sean Owen
* @author William Rucklidge
* @author sanfordsquires
*/
public final class ReedSolomonDecoder {
private final GenericGF field;
public ReedSolomonDecoder(GenericGF field) {
this.field = field;
}
/**
* <p>Decodes given set of received codewords, which include both data and error-correction
* codewords. Really, this means it uses Reed-Solomon to detect and correct errors, in-place,
* in the input.</p>
*
* @param received data and error-correction codewords
* @param twoS number of error-correction codewords available
* @throws ReedSolomonException if decoding fails for any reason
*/
public void decode(int[] received, int twoS) throws ReedSolomonException {
decodeWithECCount(received, twoS);
}
/**
* <p>Decodes given set of received codewords, which include both data and error-correction
* codewords. Really, this means it uses Reed-Solomon to detect and correct errors, in-place,
* in the input.</p>
*
* @param received data and error-correction codewords
* @param twoS number of error-correction codewords available
* @return the number of errors corrected
* @throws ReedSolomonException if decoding fails for any reason
*/
public int decodeWithECCount(int[] received, int twoS) throws ReedSolomonException {
GenericGFPoly poly = new GenericGFPoly(field, received);
int[] syndromeCoefficients = new int[twoS];
boolean noError = true;
for (int i = 0; i < twoS; i++) {
int eval = poly.evaluateAt(field.exp(i + field.getGeneratorBase()));
syndromeCoefficients[syndromeCoefficients.length - 1 - i] = eval;
if (eval != 0) {
noError = false;
}
}
if (noError) {
return 0;
}
GenericGFPoly syndrome = new GenericGFPoly(field, syndromeCoefficients);
GenericGFPoly[] sigmaOmega =
runEuclideanAlgorithm(field.buildMonomial(twoS, 1), syndrome, twoS);
GenericGFPoly sigma = sigmaOmega[0];
GenericGFPoly omega = sigmaOmega[1];
int[] errorLocations = findErrorLocations(sigma);
int[] errorMagnitudes = findErrorMagnitudes(omega, errorLocations);
for (int i = 0; i < errorLocations.length; i++) {
int position = received.length - 1 - field.log(errorLocations[i]);
if (position < 0) {
throw new ReedSolomonException("Bad error location");
}
received[position] = GenericGF.addOrSubtract(received[position], errorMagnitudes[i]);
}
return errorLocations.length;
}
private GenericGFPoly[] runEuclideanAlgorithm(GenericGFPoly a, GenericGFPoly b, int R)
throws ReedSolomonException {
// Assume a's degree is >= b's
if (a.getDegree() < b.getDegree()) {
GenericGFPoly temp = a;
a = b;
b = temp;
}
GenericGFPoly rLast = a;
GenericGFPoly r = b;
GenericGFPoly tLast = field.getZero();
GenericGFPoly t = field.getOne();
// Run Euclidean algorithm until r's degree is less than R/2
while (2 * r.getDegree() >= R) {
GenericGFPoly rLastLast = rLast;
GenericGFPoly tLastLast = tLast;
rLast = r;
tLast = t;
// Divide rLastLast by rLast, with quotient in q and remainder in r
if (rLast.isZero()) {
// Oops, Euclidean algorithm already terminated?
throw new ReedSolomonException("r_{i-1} was zero");
}
r = rLastLast;
GenericGFPoly q = field.getZero();
int denominatorLeadingTerm = rLast.getCoefficient(rLast.getDegree());
int dltInverse = field.inverse(denominatorLeadingTerm);
while (r.getDegree() >= rLast.getDegree() && !r.isZero()) {
int degreeDiff = r.getDegree() - rLast.getDegree();
int scale = field.multiply(r.getCoefficient(r.getDegree()), dltInverse);
q = q.addOrSubtract(field.buildMonomial(degreeDiff, scale));
r = r.addOrSubtract(rLast.multiplyByMonomial(degreeDiff, scale));
}
t = q.multiply(tLast).addOrSubtract(tLastLast);
if (r.getDegree() >= rLast.getDegree()) {
throw new IllegalStateException("Division algorithm failed to reduce polynomial? " +
"r: " + r + ", rLast: " + rLast);
}
}
int sigmaTildeAtZero = t.getCoefficient(0);
if (sigmaTildeAtZero == 0) {
throw new ReedSolomonException("sigmaTilde(0) was zero");
}
int inverse = field.inverse(sigmaTildeAtZero);
GenericGFPoly sigma = t.multiply(inverse);
GenericGFPoly omega = r.multiply(inverse);
return new GenericGFPoly[]{sigma, omega};
}
private int[] findErrorLocations(GenericGFPoly errorLocator) throws ReedSolomonException {
// This is a direct application of Chien's search
int numErrors = errorLocator.getDegree();
if (numErrors == 1) { // shortcut
return new int[] { errorLocator.getCoefficient(1) };
}
int[] result = new int[numErrors];
int e = 0;
for (int i = 1; i < field.getSize() && e < numErrors; i++) {
if (errorLocator.evaluateAt(i) == 0) {
result[e] = field.inverse(i);
e++;
}
}
if (e != numErrors) {
throw new ReedSolomonException("Error locator degree does not match number of roots");
}
return result;
}
private int[] findErrorMagnitudes(GenericGFPoly errorEvaluator, int[] errorLocations) {
// This is directly applying Forney's Formula
int s = errorLocations.length;
int[] result = new int[s];
for (int i = 0; i < s; i++) {
int xiInverse = field.inverse(errorLocations[i]);
int denominator = 1;
for (int j = 0; j < s; j++) {
if (i != j) {
//denominator = field.multiply(denominator,
// GenericGF.addOrSubtract(1, field.multiply(errorLocations[j], xiInverse)));
// Above should work but fails on some Apple and Linux JDKs due to a Hotspot bug.
// Below is a funny-looking workaround from Steven Parkes
int term = field.multiply(errorLocations[j], xiInverse);
int termPlus1 = (term & 0x1) == 0 ? term | 1 : term & ~1;
denominator = field.multiply(denominator, termPlus1);
}
}
result[i] = field.multiply(errorEvaluator.evaluateAt(xiInverse),
field.inverse(denominator));
if (field.getGeneratorBase() != 0) {
result[i] = field.multiply(result[i], xiInverse);
}
}
return result;
}
}