zxing/csharp/common/reedsolomon/ReedSolomonDecoder.cs

/*
* 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.
*/

using System;
namespace com.google.zxing.common.reedsolomon
{

    /// <summary> <p>Implements Reed-Solomon decoding, as the name implies.</p>
    /// 
    /// <p>The algorithm will not be explained here, but the following references were helpful
    /// in creating this implementation:</p>
    /// 
    /// <ul>
    /// <li>Bruce Maggs.
    /// <a href="http://www.cs.cmu.edu/afs/cs.cmu.edu/project/pscico-guyb/realworld/www/rs_decode.ps">
    /// "Decoding Reed-Solomon Codes"</a> (see discussion of Forney's Formula)</li>
    /// <li>J.I. Hall. <a href="www.mth.msu.edu/~jhall/classes/codenotes/GRS.pdf">
    /// "Chapter 5. Generalized Reed-Solomon Codes"</a>
    /// (see discussion of Euclidean algorithm)</li>
    /// </ul>
    /// 
    /// <p>Much credit is due to William Rucklidge since portions of this code are an indirect
    /// port of his C++ Reed-Solomon implementation.</p>
    /// 
    /// </summary>
    /// <author>  srowen@google.com (Sean Owen)
    /// </author>
    /// <author>  William Rucklidge
    /// </author>
    public sealed class ReedSolomonDecoder
    {
          private GF256 field;

          public ReedSolomonDecoder(GF256 field) {
            this.field = field;
          }

          /**
           * <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>
           *
           * @param received data and error-correction codewords
           * @param twoS number of error-correction codewords available
           * @throws ReedSolomonException if decoding fails for any reason
           */
          public void decode(int[] received, int twoS) {
              try{
              
              
                GF256Poly poly = new GF256Poly(field, received);
                int[] syndromeCoefficients = new int[twoS];
                bool dataMatrix = field.Equals(GF256.DATA_MATRIX_FIELD);
                bool noError = true;
                for (int i = 0; i < twoS; i++) {
                  // Thanks to sanfordsquires for this fix:
                  int eval = poly.evaluateAt(field.exp(dataMatrix ? i + 1 : i));
                  syndromeCoefficients[syndromeCoefficients.Length - 1 - i] = eval;
                  if (eval != 0) {
                    noError = false;
                  }
                }
                if (noError) {
                  return;
                }
                GF256Poly syndrome = new GF256Poly(field, syndromeCoefficients);
                GF256Poly[] sigmaOmega =
                    runEuclideanAlgorithm(field.buildMonomial(twoS, 1), syndrome, twoS);
                GF256Poly sigma = sigmaOmega[0];
                GF256Poly omega = sigmaOmega[1];
                int[] errorLocations = findErrorLocations(sigma);
                int[] errorMagnitudes = findErrorMagnitudes(omega, errorLocations, dataMatrix);
                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");
                  }
                  received[position] = GF256.addOrSubtract(received[position], errorMagnitudes[i]);
                }
              }catch(ReedSolomonException e){
                throw new ReedSolomonException(e.Message);
              }
          }

          private GF256Poly[] runEuclideanAlgorithm(GF256Poly a, GF256Poly b, int R){
            // Assume a's degree is >= b's
            if (a.getDegree() < b.getDegree()) {
              GF256Poly temp = a;
              a = b;
              b = temp;
            }

            GF256Poly rLast = a;
            GF256Poly r = b;
            GF256Poly sLast = field.getOne();
            GF256Poly s = field.getZero();
            GF256Poly tLast = field.getZero();
            GF256Poly t = field.getOne();

            // Run Euclidean algorithm until r's degree is less than R/2
            while (r.getDegree() >= R / 2) {
              GF256Poly rLastLast = rLast;
              GF256Poly sLastLast = sLast;
              GF256Poly tLastLast = tLast;
              rLast = r;
              sLast = s;
              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");
              }
              r = rLastLast;
              GF256Poly q = field.getZero();
              int denominatorLeadingTerm = rLast.getCoefficient(rLast.getDegree());
              int dltInverse = field.inverse(denominatorLeadingTerm);
              while (r.getDegree() >= rLast.getDegree() && !r.isZero()) {
                int degreeDiff = r.getDegree() - rLast.getDegree();
                int scale = field.multiply(r.getCoefficient(r.getDegree()), dltInverse);
                q = q.addOrSubtract(field.buildMonomial(degreeDiff, scale));
                r = r.addOrSubtract(rLast.multiplyByMonomial(degreeDiff, scale));
              }

              s = q.multiply(sLast).addOrSubtract(sLastLast);
              t = q.multiply(tLast).addOrSubtract(tLastLast);
            }

            int sigmaTildeAtZero = t.getCoefficient(0);
            if (sigmaTildeAtZero == 0) {
              throw new ReedSolomonException("sigmaTilde(0) was zero");
            }

            int inverse = field.inverse(sigmaTildeAtZero);
            GF256Poly sigma = t.multiply(inverse);
            GF256Poly omega = r.multiply(inverse);
            return new GF256Poly[]{sigma, omega};
          }

          private int[] findErrorLocations(GF256Poly errorLocator){
            // This is a direct application of Chien's search
            int numErrors = errorLocator.getDegree();
            if (numErrors == 1) { // shortcut
              return new int[] { errorLocator.getCoefficient(1) };
            }
            int[] result = new int[numErrors];
            int e = 0;
            for (int i = 1; i < 256 && 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 result;
          }

          private int[] findErrorMagnitudes(GF256Poly errorEvaluator, int[] errorLocations, bool dataMatrix) {
            // 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,
                      GF256.addOrSubtract(1, field.multiply(errorLocations[j], xiInverse)));
                }
              }
              result[i] = field.multiply(errorEvaluator.evaluateAt(xiInverse),
                  field.inverse(denominator));
              // Thanks to sanfordsquires for this fix:
              if (dataMatrix) {
                result[i] = field.multiply(result[i], xiInverse);
              }
            }
            return result;
          }
    
    }
}