/// <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); }
internal GenericGFPoly[] Divide(GenericGFPoly other) { if (field.Equals(other.field) == false) { throw new ArgumentException("GenericGFPolys do not have same GenericGF field"); } if (other.IsZero) { throw new ArgumentException("Divide by 0"); } GenericGFPoly quotient = field.Zero; 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 = field.BuildMonomial(degreeDifference, scale); quotient = quotient.AddOrSubtract(iterationQuotient); remainder = remainder.AddOrSubtract(term); } return(new GenericGFPoly[] { quotient, remainder }); }