/// <summary>
/// Finds the error magnitudes by directly applying Forney's Formula
/// </summary>
/// <returns>The error magnitudes.</returns>
/// <param name="errorEvaluator">Error evaluator.</param>
/// <param name="errorLocator">Error locator.</param>
/// <param name="errorLocations">Error locations.</param>
private int[] findErrorMagnitudes(ModulusPoly errorEvaluator,
ModulusPoly errorLocator,
int[] errorLocations)
{
int errorLocatorDegree = errorLocator.Degree;
if (errorLocatorDegree < 1)
{
return(new int[0]);
}
int[] formalDerivativeCoefficients = new int[errorLocatorDegree];
for (int i = 1; i <= errorLocatorDegree; i++)
{
formalDerivativeCoefficients[errorLocatorDegree - i] =
field.multiply(i, errorLocator.getCoefficient(i));
}
ModulusPoly formalDerivative = new ModulusPoly(field, formalDerivativeCoefficients);
// 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 numerator = field.subtract(0, errorEvaluator.evaluateAt(xiInverse));
int denominator = field.inverse(formalDerivative.evaluateAt(xiInverse));
result[i] = field.multiply(numerator, denominator);
}
return(result);
}
/// <summary>
/// Decodes the specified received.
/// </summary>
/// <param name="received">The received.</param>
/// <param name="numECCodewords">The num EC codewords.</param>
/// <param name="erasures">The erasures.</param>
/// <returns></returns>
public bool decode(int[] received, int numECCodewords, int[] erasures)
{
ModulusPoly poly = new ModulusPoly(field, received);
int[] S = new int[numECCodewords];
bool error = false;
for (int i = numECCodewords; i > 0; i--)
{
int eval = poly.evaluateAt(field.exp(i));
S[numECCodewords - i] = eval;
if (eval != 0)
{
error = true;
}
}
if (error)
{
ModulusPoly knownErrors = field.getOne();
foreach (int erasure in erasures)
{
int b = field.exp(received.Length - 1 - erasure);
// Add (1 - bx) term:
ModulusPoly term = new ModulusPoly(field, new int[] { field.subtract(0, b), 1 });
knownErrors = knownErrors.multiply(term);
}
ModulusPoly syndrome = new ModulusPoly(field, S);
//syndrome = syndrome.multiply(knownErrors);
ModulusPoly[] sigmaOmega =
runEuclideanAlgorithm(field.buildMonomial(numECCodewords, 1), syndrome, numECCodewords);
if (sigmaOmega == null)
return false;
ModulusPoly sigma = sigmaOmega[0];
ModulusPoly omega = sigmaOmega[1];
//sigma = sigma.multiply(knownErrors);
int[] errorLocations = findErrorLocations(sigma);
if (errorLocations == null)
return false;
int[] errorMagnitudes = findErrorMagnitudes(omega, sigma, errorLocations);
if (errorMagnitudes == null)
return false;
for (int i = 0; i < errorLocations.Length; i++)
{
int position = received.Length - 1 - field.log(errorLocations[i]);
if (position < 0)
{
return false;
}
received[position] = field.subtract(received[position], errorMagnitudes[i]);
}
}
return true;
}
/// <summary>
/// Finds the error locations as a direct application of Chien's search
/// </summary>
/// <returns>The error locations.</returns>
/// <param name="errorLocator">Error locator.</param>
private int[] findErrorLocations(ModulusPoly errorLocator)
{
// This is a direct application of Chien's search
int numErrors = errorLocator.Degree;
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)
{
return(null);
}
return(result);
}
/// <summary>
/// Decodes the specified received.
/// </summary>
/// <param name="received">received codewords</param>
/// <param name="numECCodewords">number of those codewords used for EC</param>
/// <param name="erasures">location of erasures</param>
/// <param name="errorLocationsCount">The error locations count.</param>
/// <returns></returns>
public bool decode(int[] received, int numECCodewords, int[] erasures, out int errorLocationsCount)
{
ModulusPoly poly = new ModulusPoly(field, received);
int[] S = new int[numECCodewords];
bool error = false;
errorLocationsCount = 0;
for (int i = numECCodewords; i > 0; i--)
{
int eval = poly.evaluateAt(field.exp(i));
S[numECCodewords - i] = eval;
if (eval != 0)
{
error = true;
}
}
if (!error)
{
return(true);
}
ModulusPoly knownErrors = field.One;
if (erasures != null)
{
foreach (int erasure in erasures)
{
int b = field.exp(received.Length - 1 - erasure);
// Add (1 - bx) term:
ModulusPoly term = new ModulusPoly(field, new int[] { field.subtract(0, b), 1 });
knownErrors = knownErrors.multiply(term);
}
}
ModulusPoly syndrome = new ModulusPoly(field, S);
//syndrome = syndrome.multiply(knownErrors);
ModulusPoly[] sigmaOmega = runEuclideanAlgorithm(field.buildMonomial(numECCodewords, 1), syndrome, numECCodewords);
if (sigmaOmega == null)
{
return(false);
}
ModulusPoly sigma = sigmaOmega[0];
ModulusPoly omega = sigmaOmega[1];
if (sigma == null || omega == null)
{
return(false);
}
//sigma = sigma.multiply(knownErrors);
int[] errorLocations = findErrorLocations(sigma);
if (errorLocations == null)
{
return(false);
}
int[] errorMagnitudes = findErrorMagnitudes(omega, sigma, errorLocations);
for (int i = 0; i < errorLocations.Length; i++)
{
int position = received.Length - 1 - field.log(errorLocations[i]);
if (position < 0)
{
return(false);
}
received[position] = field.subtract(received[position], errorMagnitudes[i]);
}
errorLocationsCount = errorLocations.Length;
return(true);
}
/// <summary>
/// Finds the error magnitudes by directly applying Forney's Formula
/// </summary>
/// <returns>The error magnitudes.</returns>
/// <param name="errorEvaluator">Error evaluator.</param>
/// <param name="errorLocator">Error locator.</param>
/// <param name="errorLocations">Error locations.</param>
private int[] findErrorMagnitudes(ModulusPoly errorEvaluator,
ModulusPoly errorLocator,
int[] errorLocations)
{
int errorLocatorDegree = errorLocator.Degree;
int[] formalDerivativeCoefficients = new int[errorLocatorDegree];
for (int i = 1; i <= errorLocatorDegree; i++)
{
formalDerivativeCoefficients[errorLocatorDegree - i] =
field.multiply(i, errorLocator.getCoefficient(i));
}
ModulusPoly formalDerivative = new ModulusPoly(field, formalDerivativeCoefficients);
// 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 numerator = field.subtract(0, errorEvaluator.evaluateAt(xiInverse));
int denominator = field.inverse(formalDerivative.evaluateAt(xiInverse));
result[i] = field.multiply(numerator, denominator);
}
return result;
}
/// <summary>
/// Finds the error locations as a direct application of Chien's search
/// </summary>
/// <returns>The error locations.</returns>
/// <param name="errorLocator">Error locator.</param>
private int[] findErrorLocations(ModulusPoly errorLocator)
{
// This is a direct application of Chien's search
int numErrors = errorLocator.Degree;
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)
{
return null;
}
return result;
}