michaelschiemer/tests/debug/test-reed-solomon-decoder.php

<?php

declare(strict_types=1);

require_once __DIR__ . '/../../vendor/autoload.php';

use App\Framework\QrCode\ErrorCorrection\ReedSolomonEncoder;

echo "=== Reed-Solomon Decoder Test ===\n\n";

// Simple Reed-Solomon decoder for verification
// This implements a basic syndrome calculation

class SimpleRSDecoder
{
    private array $gfLog;
    private array $gfExp;

    public function __construct()
    {
        $this->initializeGaloisField();
    }

    private function initializeGaloisField(): void
    {
        $this->gfLog = array_fill(0, 256, 0);
        $this->gfExp = array_fill(0, 512, 0);

        $x = 1;
        for ($i = 0; $i < 255; $i++) {
            $this->gfExp[$i] = $x;
            $this->gfLog[$x] = $i;
            $x <<= 1;
            if ($x & 0x100) {
                $x ^= 0x11d;
            }
        }

        for ($i = 255; $i < 512; $i++) {
            $this->gfExp[$i] = $this->gfExp[$i - 255];
        }
    }

    private function gfMultiply(int $a, int $b): int
    {
        if ($a === 0 || $b === 0) {
            return 0;
        }
        return $this->gfExp[$this->gfLog[$a] + $this->gfLog[$b]];
    }

    /**
     * Calculate syndromes for the received codeword
     * For a valid codeword, all syndromes should be zero
     * 
     * Standard Reed-Solomon: c(x) = c[0] + c[1]*x + c[2]*x^2 + ... + c[n-1]*x^(n-1)
     * Evaluate at generator roots: S[i] = c(α^i)
     */
    public function calculateSyndromes(array $codeword, int $ecCodewords): array
    {
        $syndromes = array_fill(0, $ecCodewords, 0);

        // Evaluate at generator roots (α^0, α^1, ..., α^(t-1))
        for ($i = 0; $i < $ecCodewords; $i++) {
            $syndrome = 0;
            $alphaPower = $this->gfExp[$i]; // α^i

            // Evaluate polynomial at α^i: sum(codeword[j] * (α^i)^j)
            $power = 1; // (α^i)^0 = 1
            for ($j = 0; $j < count($codeword); $j++) {
                $syndrome ^= $this->gfMultiply($codeword[$j], $power);
                $power = $this->gfMultiply($power, $alphaPower);
            }

            $syndromes[$i] = $syndrome;
        }

        return $syndromes;
    }

    /**
     * Check if codeword is valid (all syndromes are zero)
     */
    public function isValid(array $codeword, int $ecCodewords): bool
    {
        $syndromes = $this->calculateSyndromes($codeword, $ecCodewords);
        foreach ($syndromes as $syndrome) {
            if ($syndrome !== 0) {
                return false;
            }
        }
        return true;
    }
}

// Test with our QR code data
echo "Test with QR Code Data:\n\n";

$dataCodewords = [64, 180, 132, 84, 196, 196, 242, 5, 116, 245, 36, 196, 64, 236, 17, 236];
$rs = new ReedSolomonEncoder();
$ecCodewords = $rs->encode($dataCodewords, 10);

echo "Data codewords (16): " . implode(', ', $dataCodewords) . "\n";
echo "EC codewords (10): " . implode(', ', $ecCodewords) . "\n\n";

// Create full codeword
$fullCodeword = array_merge($dataCodewords, $ecCodewords);

echo "Full codeword (26): " . implode(', ', $fullCodeword) . "\n\n";

// Decode and verify
$decoder = new SimpleRSDecoder();
$syndromes = $decoder->calculateSyndromes($fullCodeword, 10);

echo "Syndromes (should all be 0 for valid codeword):\n";
$allZero = true;
for ($i = 0; $i < count($syndromes); $i++) {
    $status = $syndromes[$i] === 0 ? '✅' : '❌';
    if ($syndromes[$i] !== 0) {
        $allZero = false;
    }
    echo "  S[{$i}] = {$syndromes[$i]} {$status}\n";
}

echo "\n";

if ($allZero) {
    echo "✅ All syndromes are zero - Reed-Solomon codeword is VALID!\n";
    echo "\nThis means the EC codewords are correct.\n";
    echo "If the QR code still doesn't scan, the issue is NOT in Reed-Solomon.\n";
} else {
    echo "❌ Some syndromes are non-zero - Reed-Solomon codeword is INVALID!\n";
    echo "\nThis means the EC codewords are incorrect.\n";
    echo "The Reed-Solomon implementation has a bug.\n";
}

// Test with corrupted data
echo "\n=== Test with Corrupted Data ===\n";
$corruptedCodeword = $fullCodeword;
$corruptedCodeword[0] ^= 1; // Flip one bit

$corruptedSyndromes = $decoder->calculateSyndromes($corruptedCodeword, 10);

echo "Corrupted codeword (bit 0 flipped):\n";
$corruptedAllZero = true;
for ($i = 0; $i < count($corruptedSyndromes); $i++) {
    if ($corruptedSyndromes[$i] !== 0) {
        $corruptedAllZero = false;
    }
    echo "  S[{$i}] = {$corruptedSyndromes[$i]}\n";
}

if ($corruptedAllZero) {
    echo "❌ Corrupted codeword appears valid (decoder bug)\n";
} else {
    echo "✅ Corrupted codeword correctly detected as invalid\n";
}