コード例 #1
0
        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 });
        }
コード例 #2
0
        public void Initialize()
        {
            expTable = new int[size];
            logTable = new int[size];

            int x = 1;

            for (int i = 0; i < size; i++)
            {
                expTable[i] = x;
                x         <<= 1; // x = x * 2; we're assuming the generator alpha is 2
                if (x >= size)
                {
                    x ^= primitive;
                    x &= size - 1;
                }
            }

            for (int i = 0; i < size - 1; i++)
            {
                logTable[expTable[i]] = i;
            }

            // logTable[0] == 0 but this should never be used
            zero = new GenericGFPoly(this, new int[] { 0 });
            one  = new GenericGFPoly(this, new int[] { 1 });

            initialized = true;
        }
コード例 #3
0
        public void Encode(int[] toEncode, int ecBytes)
        {
            if (ecBytes == 0)
            {
                throw new ArgumentException("No error correction bytes");
            }

            int dataBytes = toEncode.Length - ecBytes;

            if (dataBytes <= 0)
            {
                throw new ArgumentException("No data bytes provided");
            }

            GenericGFPoly generator        = BuildGenerator(ecBytes);
            var           infoCoefficients = new int[dataBytes];

            Array.Copy(toEncode, 0, infoCoefficients, 0, dataBytes);

            var info = new GenericGFPoly(field, infoCoefficients);

            info = info.MultiplyByMonomial(ecBytes, 1);

            GenericGFPoly remainder = info.Divide(generator)[1];

            int[] coefficients        = remainder.Coefficients;
            int   numZeroCoefficients = ecBytes - coefficients.Length;

            for (var i = 0; i < numZeroCoefficients; i++)
            {
                toEncode[dataBytes + i] = 0;
            }

            Array.Copy(coefficients, 0, toEncode, dataBytes + numZeroCoefficients, coefficients.Length);
        }
コード例 #4
0
        internal GenericGFPoly Multiply(GenericGFPoly other)
        {
            if (field.Equals(other.field) == false)
            {
                throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
            }

            if (IsZero || other.IsZero)
            {
                return(field.Zero);
            }

            int[] aCoefficients = 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));
        }
コード例 #5
0
        // this method has been added by Sebastien ROBERT
        // this implementation makes the mathematician-friendly approach programmer-friendly
        public byte[] EncodeEx(byte[] toEncode, int ecBytes)
        {
            if (ecBytes == 0)
            {
                throw new ArgumentException("No error correction bytes");
            }

            int dataBytes = toEncode.Length - ecBytes;

            if (dataBytes <= 0)
            {
                throw new ArgumentException("No data bytes provided");
            }

            GenericGFPoly generator = BuildGenerator(ecBytes);

            int[] infoCoefficients = toEncode.Select(x => (int)x).ToArray();

            var info = new GenericGFPoly(field, infoCoefficients);

            info = info.MultiplyByMonomial(ecBytes, 1);

            GenericGFPoly remainder = info.Divide(generator)[1];

            int[] coefficients        = remainder.Coefficients;
            int   numZeroCoefficients = ecBytes - coefficients.Length;

            return(Enumerable.Repeat <byte>(0, numZeroCoefficients)
                   .Concat(coefficients.Select(x => (byte)x))
                   .ToArray());
        }
コード例 #6
0
        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);
        }
コード例 #7
0
        /// <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);
        }
コード例 #8
0
        private GenericGFPoly BuildGenerator(int degree)
        {
            if (degree >= cachedGenerators.Count)
            {
                GenericGFPoly 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) }));
                    cachedGenerators.Add(nextGenerator);
                    lastGenerator = nextGenerator;
                }
            }

            return(cachedGenerators[degree]);
        }
コード例 #9
0
        internal GenericGFPoly AddOrSubtract(GenericGFPoly other)
        {
            if (field.Equals(other.field) == false)
            {
                throw new ArgumentException("GenericGFPolys do not have same GenericGF field");
            }

            if (IsZero)
            {
                return(other);
            }

            if (other.IsZero)
            {
                return(this);
            }

            int[] smallerCoefficients = 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));
        }
コード例 #10
0
        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)));
                        // Above should work but fails on some Apple and Linux JDKs due to a Hotspot bug.
                        // Below is a funny-looking workaround from Steven Parkes
                        int term      = field.Multiply(errorLocations[j], xiInverse);
                        int termPlus1 = (term & 0x1) == 0 ? term | 1 : term & ~1;
                        denominator = field.Multiply(denominator, termPlus1);

                        // removed in java version, not sure if this is right
                        // denominator = field.multiply(denominator, GenericGF.addOrSubtract(1, field.multiply(errorLocations[j], xiInverse)));
                    }
                }

                result[i] = field.Multiply(errorEvaluator.EvaluateAt(xiInverse), field.Inverse(denominator));

                if (field.GeneratorBase != 0)
                {
                    result[i] = field.Multiply(result[i], xiInverse);
                }
            }

            return(result);
        }
コード例 #11
0
        internal GenericGFPoly[] RunEuclideanAlgorithm(GenericGFPoly a, GenericGFPoly b, int R)
        {
            // Assume a's degree is >= b's
            if (a.Degree < b.Degree)
            {
                GenericGFPoly temp = a;
                a = b;
                b = temp;
            }

            GenericGFPoly rLast = a;
            GenericGFPoly r     = b;
            GenericGFPoly tLast = field.Zero;
            GenericGFPoly t     = field.One;

            int halfR = R / 2;

            // Run Euclidean algorithm until r's degree is less than R/2
            while (r.Degree >= halfR)
            {
                GenericGFPoly rLastLast = rLast;
                GenericGFPoly 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?
                    // throw new ReedSolomonException("r_{i-1} was zero");
                    return(null);
                }

                r = rLastLast;

                GenericGFPoly 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.AddOrSubtract(field.BuildMonomial(degreeDiff, scale));
                    r = r.AddOrSubtract(rLast.MultiplyByMonomial(degreeDiff, scale));
                }

                t = q.Multiply(tLast).AddOrSubtract(tLastLast);

                if (r.Degree >= rLast.Degree)
                {
                    // throw new IllegalStateException("Division algorithm failed to reduce polynomial?");
                    return(null);
                }
            }

            int sigmaTildeAtZero = t.GetCoefficient(0);

            if (sigmaTildeAtZero == 0)
            {
                // throw new ReedSolomonException("sigmaTilde(0) was zero");
                return(null);
            }

            int           inverse = field.Inverse(sigmaTildeAtZero);
            GenericGFPoly sigma   = t.Multiply(inverse);
            GenericGFPoly omega   = r.Multiply(inverse);

            return(new GenericGFPoly[] { sigma, omega });
        }