private int[] FindErrorLocations(GenericGFPoly errorLocator)
{
// This is a direct application of Chien's search
int numErrors = errorLocator.Degree;
if (numErrors == 1)
{
// shortcut
return(new int[] { errorLocator.GetCoefficient(1) });
}
int[] result = new int[numErrors];
int e = 0;
for (int i = 1; i < field.Size && 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(null);
}
return(result);
}
/// <summary>
/// <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>
/// </summary>
/// <param name="received">data and error-correction codewords</param>
/// <param name="twoS">number of error-correction codewords available</param>
/// <returns>false: decoding fails</returns>
public bool Decode(int[] received, int twoS)
{
var poly = new GenericGFPoly(field, received);
var syndromeCoefficients = new int[twoS];
var noError = true;
for (var i = 0; i < twoS; i++)
{
int eval = poly.EvaluateAt(field.Exp(i + field.GeneratorBase));
syndromeCoefficients[syndromeCoefficients.Length - 1 - i] = eval;
if (eval != 0)
{
noError = false;
}
}
if (noError)
{
return(true);
}
var syndrome = new GenericGFPoly(field, syndromeCoefficients);
GenericGFPoly[] sigmaOmega = RunEuclideanAlgorithm(field.BuildMonomial(twoS, 1), syndrome, twoS);
if (sigmaOmega == null)
{
return(false);
}
GenericGFPoly sigma = sigmaOmega[0];
int[] errorLocations = FindErrorLocations(sigma);
if (errorLocations == null)
{
return(false);
}
GenericGFPoly omega = sigmaOmega[1];
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");
return(false);
}
received[position] = GenericGF.AddOrSubtract(received[position], errorMagnitudes[i]);
}
return(true);
}
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);
// removed in java version, not sure if this is right
// denominator = field.multiply(denominator, GenericGF.addOrSubtract(1, field.multiply(errorLocations[j], xiInverse)));
}
}
result[i] = field.Multiply(errorEvaluator.EvaluateAt(xiInverse), field.Inverse(denominator));
if (field.GeneratorBase != 0)
{
result[i] = field.Multiply(result[i], xiInverse);
}
}
return(result);
}