zxing/csharp/common/reedsolomon/ReedSolomonDecoder.cs
srowen d4efd44fb0 New C# port from Suraj Supekar
git-svn-id: https://zxing.googlecode.com/svn/trunk@1202 59b500cc-1b3d-0410-9834-0bbf25fbcc57
2010-02-05 19:52:53 +00:00

217 lines
7 KiB
C#
Executable file

/*
* 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;
}
}
}