zxing/csharp/common/reedsolomon/ReedSolomonDecoder.cs

/*
* 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.
*/
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>  Sean Owen
	/// </author>
	/// <author>  William Rucklidge
	/// </author>
	/// <author>  sanfordsquires
	/// </author>
	/// <author>www.Redivivus.in (suraj.supekar@redivivus.in) - Ported from ZXING Java Source 
	/// </author>
	public sealed class ReedSolomonDecoder
	{
		
		//UPGRADE_NOTE: Final was removed from the declaration of 'field '. "ms-help://MS.VSCC.v80/dv_commoner/local/redirect.htm?index='!DefaultContextWindowIndex'&keyword='jlca1003'"
		private GF256 field;
		
		public ReedSolomonDecoder(GF256 field)
		{
			this.field = field;
		}
		
		/// <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>
		/// <throws>  ReedSolomonException if decoding fails for any reason </throws>
		public void  decode(int[] received, int twoS)
		{
			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]);
			}
		}
		
		private GF256Poly[] runEuclideanAlgorithm(GF256Poly a, GF256Poly b, int R)
		{
			// Assume a's degree is >= b's
			if (a.Degree < b.Degree)
			{
				GF256Poly temp = a;
				a = b;
				b = temp;
			}
			
			GF256Poly rLast = a;
			GF256Poly r = b;
			GF256Poly sLast = field.One;
			GF256Poly s = field.Zero;
			GF256Poly tLast = field.Zero;
			GF256Poly t = field.One;
			
			// Run Euclidean algorithm until r's degree is less than R/2
			while (r.Degree >= 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.Zero)
				{
					// Oops, Euclidean algorithm already terminated?
					throw new ReedSolomonException("r_{i-1} was zero");
				}
				r = rLastLast;
				GF256Poly q = field.Zero;
				int denominatorLeadingTerm = rLast.getCoefficient(rLast.Degree);
				int dltInverse = field.inverse(denominatorLeadingTerm);
				while (r.Degree >= rLast.Degree && !r.Zero)
				{
					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));
				}
				
				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.Degree;
			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;
		}
	}
}