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<?php
/*
* 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;
/**
* <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>
*
* @author Sean Owen
* @author William Rucklidge
* @author sanfordsquires
*/
final class ReedSolomonDecoder
{
private $field;
public function __construct($field)
{
$this->field = $field;
}
/**
* <p>Decodes given set of received codewords, which include both data and error-correction
* codewords. Really, this means it uses Reed-Solomon to detect and correct errors, in-place,
* in the input.</p>
*
* @param received data and error-correction codewords
* @param twoS number of error-correction codewords available
*
* @throws ReedSolomonException if decoding fails for any reason
*/
public function decode(&$received, $twoS)
{
$poly = new GenericGFPoly($this->field, $received);
$syndromeCoefficients = fill_array(0, $twoS, 0);
$noError = true;
for ($i = 0; $i < $twoS; $i++) {
$eval = $poly->evaluateAt($this->field->exp($i + $this->field->getGeneratorBase()));
$syndromeCoefficients[count($syndromeCoefficients) - 1 - $i] = $eval;
if ($eval != 0) {
$noError = false;
}
}
if ($noError) {
return;
}
$syndrome = new GenericGFPoly($this->field, $syndromeCoefficients);
$sigmaOmega =
$this->runEuclideanAlgorithm($this->field->buildMonomial($twoS, 1), $syndrome, $twoS);
$sigma = $sigmaOmega[0];
$omega = $sigmaOmega[1];
$errorLocations = $this->findErrorLocations($sigma);
$errorMagnitudes = $this->findErrorMagnitudes($omega, $errorLocations);
$errorLocationsCount = count($errorLocations);
for ($i = 0; $i < $errorLocationsCount; $i++) {
$position = count($received) - 1 - $this->field->log($errorLocations[$i]);
if ($position < 0) {
throw new ReedSolomonException("Bad error location");
}
$received[$position] = GenericGF::addOrSubtract($received[$position], $errorMagnitudes[$i]);
}
}
private function runEuclideanAlgorithm($a, $b, $R)
{
// Assume a's degree is >= b's
if ($a->getDegree() < $b->getDegree()) {
$temp = $a;
$a = $b;
$b = $temp;
}
$rLast = $a;
$r = $b;
$tLast = $this->field->getZero();
$t = $this->field->getOne();
// Run Euclidean algorithm until r's degree is less than R/2
while ($r->getDegree() >= $R / 2) {
$rLastLast = $rLast;
$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");
}
$r = $rLastLast;
$q = $this->field->getZero();
$denominatorLeadingTerm = $rLast->getCoefficient($rLast->getDegree());
$dltInverse = $this->field->inverse($denominatorLeadingTerm);
while ($r->getDegree() >= $rLast->getDegree() && !$r->isZero()) {
$degreeDiff = $r->getDegree() - $rLast->getDegree();
$scale = $this->field->multiply($r->getCoefficient($r->getDegree()), $dltInverse);
$q = $q->addOrSubtract($this->field->buildMonomial($degreeDiff, $scale));
$r = $r->addOrSubtract($rLast->multiplyByMonomial($degreeDiff, $scale));
}
$t = $q->multiply($tLast)->addOrSubtract($tLastLast);
if ($r->getDegree() >= $rLast->getDegree()) {
throw new ReedSolomonException("Division algorithm failed to reduce polynomial?");
}
}
$sigmaTildeAtZero = $t->getCoefficient(0);
if ($sigmaTildeAtZero == 0) {
throw new ReedSolomonException("sigmaTilde(0) was zero");
}
$inverse = $this->field->inverse($sigmaTildeAtZero);
$sigma = $t->multiply($inverse);
$omega = $r->multiply($inverse);
return [$sigma, $omega];
}
private function findErrorLocations($errorLocator)
{
// This is a direct application of Chien's search
$numErrors = $errorLocator->getDegree();
if ($numErrors == 1) { // shortcut
return [$errorLocator->getCoefficient(1)];
}
$result = fill_array(0, $numErrors, 0);
$e = 0;
for ($i = 1; $i < $this->field->getSize() && $e < $numErrors; $i++) {
if ($errorLocator->evaluateAt($i) == 0) {
$result[$e] = $this->field->inverse($i);
$e++;
}
}
if ($e != $numErrors) {
throw new ReedSolomonException("Error locator degree does not match number of roots");
}
return $result;
}
private function findErrorMagnitudes($errorEvaluator, $errorLocations)
{
// This is directly applying Forney's Formula
$s = count($errorLocations);
$result = fill_array(0, $s, 0);
for ($i = 0; $i < $s; $i++) {
$xiInverse = $this->field->inverse($errorLocations[$i]);
$denominator = 1;
for ($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
$term = $this->field->multiply($errorLocations[$j], $xiInverse);
$termPlus1 = ($term & 0x1) == 0 ? $term | 1 : $term & ~1;
$denominator = $this->field->multiply($denominator, $termPlus1);
}
}
$result[$i] = $this->field->multiply($errorEvaluator->evaluateAt($xiInverse),
$this->field->inverse($denominator));
if ($this->field->getGeneratorBase() != 0) {
$result[$i] = $this->field->multiply($result[$i], $xiInverse);
}
}
return $result;
}
}
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