/**
* 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.
*
* @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 {
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;
}
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]);
}
}
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;
}
/**
* 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.
*
* @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 {
GenericGFPoly poly = new GenericGFPoly(field, received);
int[] syndromeCoefficients = new int[twoS];
boolean dataMatrix = field.equals(GenericGF.GenericGFs.AZTEC_DATA_8.mGf);
boolean noError = true;
for (int i = 0; i < twoS; i++) {
// Thanks to sanfordsquires for this fix:
int eval = poly.evaluateAt(field.exp(dataMatrix ? i + 1 : i));
syndromeCoefficients[syndromeCoefficients.length - 1 - i] = eval;
if (eval != 0) {
noError = false;
}
}
if (noError) {
return;
}
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, dataMatrix);
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]);
}
}
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;
}
