/// <summary>
/// Runs the euclidean algorithm (Greatest Common Divisor) until r's degree is less than R/2
/// </summary>
/// <returns>The euclidean algorithm.</returns>
private ModulusPoly[] RunEuclideanAlgorithm(ModulusPoly a, ModulusPoly b, int R)
{
// Assume a's degree is >= b's
if (a.Degree < b.Degree)
{
ModulusPoly temp = a;
a = b;
b = temp;
}
ModulusPoly rLast = a;
ModulusPoly r = b;
ModulusPoly tLast = field.Zero;
ModulusPoly t = field.One;
// Run Euclidean algorithm until r's degree is less than R/2
while (r.Degree >= R / 2)
{
ModulusPoly rLastLast = rLast;
ModulusPoly 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?
return(null);
}
r = rLastLast;
ModulusPoly q = field.Zero;
int denominatorLeadingTerm = rLast.GetCoefficient(rLast.Degree);
int dltInverse = field.Inverse(denominatorLeadingTerm);
while (r.Degree >= rLast.Degree && !r.IsZero)
{
int degreeDiff = r.Degree - rLast.Degree;
int scale = field.Multiply(r.GetCoefficient(r.Degree), dltInverse);
q = q.Add(field.BuildMonomial(degreeDiff, scale));
r = r.Subtract(rLast.MultiplyByMonomial(degreeDiff, scale));
}
t = q.Multiply(tLast).Subtract(tLastLast).GetNegative();
}
int sigmaTildeAtZero = t.GetCoefficient(0);
if (sigmaTildeAtZero == 0)
{
return(null);
}
int inverse = field.Inverse(sigmaTildeAtZero);
ModulusPoly sigma = t.Multiply(inverse);
ModulusPoly omega = r.Multiply(inverse);
return(new ModulusPoly[] { sigma, omega });
}
/// <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 int 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)
{
return(0);
}
ModulusPoly knownErrors = field.One;
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)
{
throw ReaderException.Instance;
}
ModulusPoly sigma = sigmaOmega[0];
ModulusPoly omega = sigmaOmega[1];
if (sigma == null || omega == null)
{
throw ReaderException.Instance;
}
//sigma = sigma.multiply(knownErrors);
int[] errorLocations = FindErrorLocations(sigma);
if (errorLocations == null)
{
throw ReaderException.Instance;
}
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)
{
throw ReaderException.Instance;
// return -3; // don't throw
}
received[position] = field.Subtract(received[position], errorMagnitudes[i]);
}
return(errorLocations.Length);
}