/* * Copyright 2007 ZXing authors * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. * You may obtain a copy of the License at * * http://www.apache.org/licenses/LICENSE-2.0 * * Unless required by applicable law or agreed to in writing, software * distributed under the License is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * See the License for the specific language governing permissions and * limitations under the License. */ namespace ZXing.Common.ReedSolomon { ///

Implements Reed-Solomon decoding, as the name implies.

/// ///

The algorithm will not be explained here, but the following references were helpful /// in creating this implementation:

/// /// /// ///

Much credit is due to William Rucklidge since portions of this code are an indirect /// port of his C++ Reed-Solomon implementation.

/// ///
/// Sean Owen /// William Rucklidge /// sanfordsquires public sealed class ReedSolomonDecoder { private readonly GenericGF field; public ReedSolomonDecoder(GenericGF field) { this.field = field; } /// ///

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.

///
/// data and error-correction codewords /// number of error-correction codewords available /// false: decoding fails 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++) { 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); var sigmaOmega = runEuclideanAlgorithm(field.buildMonomial(twoS, 1), syndrome, twoS); if (sigmaOmega == null) return false; var sigma = sigmaOmega[0]; var errorLocations = findErrorLocations(sigma); if (errorLocations == null) return false; var omega = sigmaOmega[1]; var errorMagnitudes = findErrorMagnitudes(omega, errorLocations); for (var i = 0; i < errorLocations.Length; i++) { var 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[] 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; // Run Euclidean algorithm until r's degree is less than R/2 while (r.Degree >= R / 2) { 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 }; } 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; } 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; } } }