rsdecoder.js

/*
  Ported to JavaScript by Lazar Laszlo 2011 
  
  lazarsoft@gmail.com, www.lazarsoft.info
  
*/

/*
*
* 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.
*/


function ReedSolomonDecoder(field)
{
	this.field = field;
	this.decode=function(received,  twoS)
	{
			var poly = new GF256Poly(this.field, received);
			var syndromeCoefficients = new Array(twoS);
			for(var i=0;i<syndromeCoefficients.length;i++)syndromeCoefficients[i]=0;
			var dataMatrix = false;//this.field.Equals(GF256.DATA_MATRIX_FIELD);
			var noError = true;
			for (var i = 0; i < twoS; i++)
			{
				// Thanks to sanfordsquires for this fix:
				var eval = poly.evaluateAt(this.field.exp(dataMatrix?i + 1:i));
				syndromeCoefficients[syndromeCoefficients.length - 1 - i] = eval;
				if (eval != 0)
				{
					noError = false;
				}
			}
			if (noError)
			{
				return ;
			}
			var syndrome = new GF256Poly(this.field, syndromeCoefficients);
			var sigmaOmega = this.runEuclideanAlgorithm(this.field.buildMonomial(twoS, 1), syndrome, twoS);
			var sigma = sigmaOmega[0];
			var omega = sigmaOmega[1];
			var errorLocations = this.findErrorLocations(sigma);
			var errorMagnitudes = this.findErrorMagnitudes(omega, errorLocations, dataMatrix);
			for (var i = 0; i < errorLocations.length; i++)
			{
				var position = received.length - 1 - this.field.log(errorLocations[i]);
				if (position < 0)
				{
					throw "ReedSolomonException Bad error location";
				}
				received[position] = GF256.addOrSubtract(received[position], errorMagnitudes[i]);
			}
	}
	
	this.runEuclideanAlgorithm=function( a,  b,  R)
		{
			// Assume a's degree is >= b's
			if (a.Degree < b.Degree)
			{
				var temp = a;
				a = b;
				b = temp;
			}
			
			var rLast = a;
			var r = b;
			var sLast = this.field.One;
			var s = this.field.Zero;
			var tLast = this.field.Zero;
			var t = this.field.One;
			
			// Run Euclidean algorithm until r's degree is less than R/2
			while (r.Degree >= Math.floor(R / 2))
			{
				var rLastLast = rLast;
				var sLastLast = sLast;
				var 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 "r_{i-1} was zero";
				}
				r = rLastLast;
				var q = this.field.Zero;
				var denominatorLeadingTerm = rLast.getCoefficient(rLast.Degree);
				var dltInverse = this.field.inverse(denominatorLeadingTerm);
				while (r.Degree >= rLast.Degree && !r.Zero)
				{
					var degreeDiff = r.Degree - rLast.Degree;
					var scale = this.field.multiply(r.getCoefficient(r.Degree), dltInverse);
					q = q.addOrSubtract(this.field.buildMonomial(degreeDiff, scale));
					r = r.addOrSubtract(rLast.multiplyByMonomial(degreeDiff, scale));
					//r.EXE();
				}
				
				s = q.multiply1(sLast).addOrSubtract(sLastLast);
				t = q.multiply1(tLast).addOrSubtract(tLastLast);
			}
			
			var sigmaTildeAtZero = t.getCoefficient(0);
			if (sigmaTildeAtZero == 0)
			{
				throw "ReedSolomonException sigmaTilde(0) was zero";
			}
			
			var inverse = this.field.inverse(sigmaTildeAtZero);
			var sigma = t.multiply2(inverse);
			var omega = r.multiply2(inverse);
			return new Array(sigma, omega);
		}
	this.findErrorLocations=function( errorLocator)
		{
			// This is a direct application of Chien's search
			var numErrors = errorLocator.Degree;
			if (numErrors == 1)
			{
				// shortcut
				return new Array(errorLocator.getCoefficient(1));
			}
			var result = new Array(numErrors);
			var e = 0;
			for (var i = 1; i < 256 && e < numErrors; i++)
			{
				if (errorLocator.evaluateAt(i) == 0)
				{
					result[e] = this.field.inverse(i);
					e++;
				}
			}
			if (e != numErrors)
			{
				throw "Error locator degree does not match number of roots";
			}
			return result;
		}
	this.findErrorMagnitudes=function( errorEvaluator,  errorLocations,  dataMatrix)
		{
			// This is directly applying Forney's Formula
			var s = errorLocations.length;
			var result = new Array(s);
			for (var i = 0; i < s; i++)
			{
				var xiInverse = this.field.inverse(errorLocations[i]);
				var denominator = 1;
				for (var j = 0; j < s; j++)
				{
					if (i != j)
					{
						denominator = this.field.multiply(denominator, GF256.addOrSubtract(1, this.field.multiply(errorLocations[j], xiInverse)));
					}
				}
				result[i] = this.field.multiply(errorEvaluator.evaluateAt(xiInverse), this.field.inverse(denominator));
				// Thanks to sanfordsquires for this fix:
				if (dataMatrix)
				{
					result[i] = this.field.multiply(result[i], xiInverse);
				}
			}
			return result;
		}
}