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);
}
// Method modified by Sonic-The-Hedgehog-LNK1123 (github.com/Sonic-The-Hedgehog-LNK1123)
// added missing "if (denominator == 0)" check
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)));
}
}
if (denominator == 0)
{
return(null);
}
result[i] = field.multiply(errorEvaluator.evaluateAt(xiInverse), field.inverse(denominator));
if (field.GeneratorBase != 0)
{
result[i] = field.multiply(result[i], xiInverse);
}
}
return(result);
}
// Method added by Sonic-The-Hedgehog-LNK1123 (github.com/Sonic-The-Hedgehog-LNK1123)
internal GenericGFPoly calculateForneySyndromes(GenericGFPoly syndromes, int[] positions, int messageLength)
{
int[] positionsReversed = new int[positions.Length];
for (int i = 0; i < positions.Length; i++)
{
positionsReversed[i] = messageLength - 1 - positions[i];
}
int forneySyndromesLength = syndromes.Coefficients.Length;
int[] syndromeCoefficients = new int[syndromes.Coefficients.Length];
Array.Copy(syndromes.Coefficients, 0, syndromeCoefficients, 0, syndromes.Coefficients.Length);
GenericGFPoly forneySyndromes = new GenericGFPoly(field, syndromeCoefficients, false);
for (int i = 0; i < positions.Length; i++)
{
int x = field.exp(positionsReversed[i]);
for (int j = 0; j < forneySyndromes.Coefficients.Length - 1; j++)
{
forneySyndromes.Coefficients[forneySyndromesLength - j - 1] = GenericGF.addOrSubtract(field.multiply(forneySyndromes.getCoefficient(j), x), forneySyndromes.getCoefficient(j + 1));
}
}
return(forneySyndromes);
}
internal GenericGFPoly[] divide(GenericGFPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
}
if (other.isZero)
{
throw new ArgumentException("Divide by 0", "other");
}
GenericGFPoly quotient = new GenericGFPoly(field, new int[] { 0 }, encoding);
GenericGFPoly remainder = this;
int denominatorLeadingTerm = other.getCoefficient(other.Degree);
int inverseDenominatorLeadingTerm = field.inverse(denominatorLeadingTerm);
while (remainder.Degree >= other.Degree && !remainder.isZero)
{
int degreeDifference = remainder.Degree - other.Degree;
int scale = field.multiply(remainder.getCoefficient(remainder.Degree), inverseDenominatorLeadingTerm);
GenericGFPoly term = other.multiplyByMonomial(degreeDifference, scale);
GenericGFPoly iterationQuotient = buildMonomial(degreeDifference, scale);
quotient = quotient.addOrSubtract(iterationQuotient);
remainder = remainder.addOrSubtract(term);
}
return(new GenericGFPoly[] { quotient, remainder });
}
internal GenericGFPoly multiply(GenericGFPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
}
if (isZero || other.isZero)
{
return(new GenericGFPoly(field, new int[] { 0 }, encoding));
}
int[] aCoefficients = this.coefficients;
int aLength = aCoefficients.Length;
int[] bCoefficients = other.coefficients;
int bLength = bCoefficients.Length;
int[] product = new int[aLength + bLength - 1];
for (int i = 0; i < aLength; i++)
{
int aCoeff = aCoefficients[i];
for (int j = 0; j < bLength; j++)
{
product[i + j] = GenericGF.addOrSubtract(product[i + j],
field.multiply(aCoeff, bCoefficients[j]));
}
}
return(new GenericGFPoly(field, product, encoding));
}
// Method added by Sonic-The-Hedgehog-LNK1123 (github.com/Sonic-The-Hedgehog-LNK1123)
private GenericGFPoly findErrataLocator(int[] errorPositions)
{
GenericGFPoly errataLocator = new GenericGFPoly(field, new int[] { 1 }, false);
foreach (int i in errorPositions)
{
errataLocator = errataLocator.multiply(new GenericGFPoly(field, new int[] { 1 }, false).addOrSubtract(new GenericGFPoly(field, new int[] { field.exp(i), 0 }, false)));
}
return(errataLocator);
}
// Method added by Sonic-The-Hedgehog-LNK1123 (github.com/Sonic-The-Hedgehog-LNK1123)
private GenericGFPoly findErrorEvaluator(GenericGFPoly syndrome, GenericGFPoly errataLocations)
{
int[] product = syndrome.multiply(errataLocations).Coefficients;
int[] target = new int[errataLocations.Coefficients.Length - 1];
Array.Copy(product, product.Length - errataLocations.Coefficients.Length + 1, target, 0, target.Length);
if (target.Length == 0)
{
return(null);
}
GenericGFPoly omega = new GenericGFPoly(field, target, false);
return(omega);
}
/// <summary>
/// Encodes given set of data codewords with Reed-Solomon.
/// </summary>
/// <param name="toEncode">data codewords and padding, the amount of padding should match
/// the number of error-correction codewords to generate. After encoding, the padding is
/// replaced with the error-correction codewords</param>
/// <param name="ecBytes">number of error-correction codewords to generate</param>
public void Encode(int[] toEncode, int ecBytes)
{
// Method modified by Sonic-The-Hedgehog-LNK1123 (github.com/Sonic-The-Hedgehog-LNK1123)
// added check for messages that are too long for the used Galois field
if (toEncode.Length >= field.Size)
{
throw new ArgumentException("Message is too long for this field", "toEncode");
}
if (ecBytes <= 0)
{
throw new ArgumentException("No error correction bytes provided", "ecBytes");
}
var dataBytes = toEncode.Length - ecBytes;
if (dataBytes <= 0)
{
throw new ArgumentException("No data bytes provided", "ecBytes");
}
var generator = buildGenerator(ecBytes);
var infoCoefficients = new int[dataBytes];
Array.Copy(toEncode, 0, infoCoefficients, 0, dataBytes);
var info = new GenericGFPoly(field, infoCoefficients, true);
info = info.multiplyByMonomial(ecBytes, 1);
var remainder = info.divide(generator)[1];
var coefficients = remainder.Coefficients;
var numZeroCoefficients = ecBytes - coefficients.Length;
for (var i = 0; i < numZeroCoefficients; i++)
{
toEncode[dataBytes + i] = 0;
}
Array.Copy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.Length);
}
// Method added by Sonic-The-Hedgehog-LNK1123 (github.com/Sonic-The-Hedgehog-LNK1123)
// this method replaces original method "runEuclideanAlgorithm"
internal GenericGFPoly runBerlekampMasseyAlgorithm(GenericGFPoly syndrome, int erasureCount)
{
GenericGFPoly sigma = new GenericGFPoly(field, new int[] { 1 }, false);
GenericGFPoly old = new GenericGFPoly(field, new int[] { 1 }, false);
for (int i = 0; i < (syndrome.Coefficients.Length - erasureCount); i++)
{
int delta = syndrome.getCoefficient(i);
for (int j = 1; j < sigma.Coefficients.Length; j++)
{
delta ^= field.multiply(sigma.getCoefficient(j), syndrome.getCoefficient(i - j));
}
List <int> oldList = new List <int>(old.Coefficients);
oldList.Add(0);
old = new GenericGFPoly(field, oldList.ToArray(), false);
if (delta != 0)
{
if (old.Coefficients.Length > sigma.Coefficients.Length)
{
GenericGFPoly new_loc = old.multiply(delta);
old = sigma.multiply(field.inverse(delta));
sigma = new_loc;
}
sigma = sigma.addOrSubtract(old.multiply(delta));
}
}
List <int> sigmaList = new List <int>(sigma.Coefficients);
while (Convert.ToBoolean(sigmaList.Count) && sigmaList[0] == 0)
{
sigmaList.RemoveAt(0);
}
sigma = new GenericGFPoly(field, sigmaList.ToArray(), false);
return(sigma);
}
internal GenericGFPoly addOrSubtract(GenericGFPoly other)
{
if (!field.Equals(other.field))
{
throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
}
if (isZero)
{
return(other);
}
if (other.isZero)
{
return(this);
}
int[] smallerCoefficients = this.coefficients;
int[] largerCoefficients = other.coefficients;
if (smallerCoefficients.Length > largerCoefficients.Length)
{
int[] temp = smallerCoefficients;
smallerCoefficients = largerCoefficients;
largerCoefficients = temp;
}
int[] sumDiff = new int[largerCoefficients.Length];
int lengthDiff = largerCoefficients.Length - smallerCoefficients.Length;
// Copy high-order terms only found in higher-degree polynomial's coefficients
Array.Copy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
for (int i = lengthDiff; i < largerCoefficients.Length; i++)
{
sumDiff[i] = GenericGF.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
}
return(new GenericGFPoly(field, sumDiff, encoding));
}
/// <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);
}