/**
* <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, $errorLocations);
for ($i = 0; $i < count($errorLocations); $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]);
}
}
if ($a == 0) {
throw new Exception();
}
return $this->expTable[$this->size - $this->logTable[$a] - 1];
}
/**
* @return product of a and b in GF(size)
*/
function multiply($a, $b)
{
if ($a == 0 || $b == 0) {
return 0;
}
return $this->expTable[($this->logTable[$a] + $this->logTable[$b]) % ($this->size - 1)];
}
public function getSize()
{
return $this->size;
}
public function getGeneratorBase()
{
return $this->generatorBase;
}
// @Override
public function toString()
{
return "GF(0x" . dechex(intval($this->primitive)) . ',' . $this->size . ')';
}
}
GenericGF::Init();
public function multiply(GenericGFPoly $other)
{
if ($other->getField() != $this->field) {
throw new \InvalidArgumentException('GenericGFPolys do not have same GenericGF field');
}
if ($this->isZero() || $other->isZero()) {
return $this->field->getZero();
}
$aCoefficients = $this->getCoefficients();
$aLength = count($aCoefficients);
$bCoefficients = $other->getCoefficients();
$bLength = count($bCoefficients);
$product = array_fill(0, $aLength + $bLength - 1, 0);
for ($i = 0; $i < $aLength; $i++) {
$aCoeff = $aCoefficients[$i];
for ($j = 0; $j < $bLength; $j++) {
$product[$i + $j] = GenericGF::addOrSubtract($product[$i + $j], $this->field->multiply($aCoeff, $bCoefficients[$j]));
}
}
return new self($this->field, $product);
}