/// <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>
/// <param name="erasurePos">array of zero-based erasure indices</param>
/// <returns>false: decoding fails</returns>
public bool Decode(int[] received, int twoS, int[]?erasurePos)
{
// Method modified by Sonic-The-Hedgehog-LNK1123 (github.com/Sonic-The-Hedgehog-LNK1123)
// to add support for erasure and errata correction
// most code ported to C# from the python code at http://en.wikiversity.org/wiki/Reed–Solomon_codes_for_coders
if (received.Length >= field.Size)
{
throw new ArgumentException("Message is too long for this field", "received");
}
if (twoS <= 0)
{
throw new ArgumentException("No error correction bytes provided", "twoS");
}
var dataBytes = received.Length - twoS;
if (dataBytes <= 0)
{
throw new ArgumentException("No data bytes provided", "twoS");
}
var syndromeCoefficients = new int[twoS];
var noError = true;
if (erasurePos == null)
{
erasurePos = new int[] { };
}
else
{
for (var i = 0; i < erasurePos.Length; i++)
{
received[erasurePos[i]] = 0;
}
}
if (erasurePos.Length > twoS)
{
return(false);
}
var poly = new GenericGFPoly(field, received, false);
for (var i = 0; i < twoS; i++)
{
var 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, false);
var forneySyndrome = calculateForneySyndromes(syndrome, erasurePos, received.Length);
var sigma = runBerlekampMasseyAlgorithm(forneySyndrome, erasurePos.Length);
if (sigma == null)
{
return(false);
}
var errorLocations = findErrorLocations(sigma);
if (errorLocations == null)
{
return(false);
}
// Prepare errors
int[] errorPositions = new int[errorLocations.Length];
for (int i = 0; i < errorLocations.Length; i++)
{
errorPositions[i] = field.log(errorLocations[i]);
}
// Prepare erasures
int[] erasurePositions = new int[erasurePos.Length];
for (int i = 0; i < erasurePos.Length; i++)
{
erasurePositions[i] = received.Length - 1 - erasurePos[i];
}
// Combine errors and erasures
int[] errataPositions = new int[errorPositions.Length + erasurePositions.Length];
Array.Copy(errorPositions, 0, errataPositions, 0, errorPositions.Length);
Array.Copy(erasurePositions, 0, errataPositions, errorPositions.Length, erasurePositions.Length);
var errataLocator = findErrataLocator(errataPositions);
var omega = findErrorEvaluator(syndrome, errataLocator);
if (omega == null)
{
return(false);
}
int[] errata = new int[errataPositions.Length];
for (int i = 0; i < errataPositions.Length; i++)
{
errata[i] = field.exp(errataPositions[i]);
}
var errorMagnitudes = findErrorMagnitudes(omega, errata);
if (errorMagnitudes == null)
{
return(false);
}
for (var i = 0; i < errata.Length; i++)
{
var position = received.Length - 1 - field.log(errata[i]);
if (position < 0)
{
// throw new ReedSolomonException("Bad error location");
return(false);
}
received[position] = GenericGF.addOrSubtract(received[position], errorMagnitudes[i]);
}
var checkPoly = new GenericGFPoly(field, received, false);
var error = false;
for (var i = 0; i < twoS; i++)
{
var eval = checkPoly.evaluateAt(field.exp(i + field.GeneratorBase));
if (eval != 0)
{
error = true;
}
}
if (error)
{
return(false);
}
return(true);
}
private GenericGFPoly buildGenerator(int degree)
{
if (degree >= cachedGenerators.Count)
{
var lastGenerator = cachedGenerators[cachedGenerators.Count - 1];
for (int d = cachedGenerators.Count; d <= degree; d++)
{
var nextGenerator = lastGenerator.multiply(new GenericGFPoly(field, new int[] { 1, field.exp(d - 1 + field.GeneratorBase) }, true));
cachedGenerators.Add(nextGenerator);
lastGenerator = nextGenerator;
}
}
return(cachedGenerators[degree]);
}