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obikmer/doc/theory/encoding/index.html
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Eric Coissac 27f5e88a7b refactor: implement RoutableSuperKmer and update k-mer indexing pipeline 
Replace raw SuperkMer routing with a new RoutableSuperKimer type that embeds canonical sequences and precomputed minimizers, enabling direct partition routing via hash. Update the build pipeline to yield RoutableSuperKmers throughout (builder, scatterer), refactor FASTA/unitig export commands to use the new type and compressed outputs (.fasta.gz, .unitigs.fasta.zst), revise SuperKmer header to store n_kmers instead of seql (avoiding 256-byte wrap), and update documentation to reflect minimizer-based theory, two evidence-encoding strategies for unitig-MPHF indexing (global offset vs. ID+rank), and the new obipipeline library architecture with parallel workers, biased scheduling, and error handling.
2026-05-01 09:33:26 +02:00

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<h1 id="dna-encoding">DNA encoding</h1>
<h2 id="2-bit-nucleotide-encoding">2-bit nucleotide encoding</h2>
<p>All nucleotides are encoded on 2 bits, MSB-first within each word. Nucleotides are numbered 0-based from the 5′ end across all sequence types:</p>
<table>
<thead>
<tr>
<th>Base</th>
<th>Encoding</th>
</tr>
</thead>
<tbody>
<tr>
<td>A</td>
<td><code>00</code></td>
</tr>
<tr>
<td>C</td>
<td><code>01</code></td>
</tr>
<tr>
<td>G</td>
<td><code>10</code></td>
</tr>
<tr>
<td>T</td>
<td><code>11</code></td>
</tr>
</tbody>
</table>
<p>The Watson-Crick complement of any base is its bitwise NOT on 2 bits: <code>complement(base) = ~base &amp; 0b11</code>.</p>
<h2 id="kmer-encoding">Kmer encoding</h2>
<p>A kmer fits in a single <code>u64</code>. Nucleotide 0 occupies bits 63–62, nucleotide i occupies bits 63−2i and 62−2i, and the low 64−2k bits are zero. Extraction of nucleotide i (0 ≤ i &lt; k): <code>(kmer &gt;&gt; (62 - 2*i)) &amp; 0b11</code>.</p>
<p>Reverse complement is computed via a <strong>16-bit lookup table</strong> (65 536 entries × 2 bytes = 128 KB, fits in L2 cache) storing the reverse-complement of every 8-base chunk.</p>
<div class="admonition abstract">
<p class="admonition-title">Algorithm — Kmer reverse complement</p>
<div class="highlight"><pre><span></span><code>procedure KmerRevcomp(kmer, k):
raw ← TABLE16[kmer &amp; 0xFFFF] &lt;&lt; 48
| TABLE16[(kmer &gt;&gt; 16) &amp; 0xFFFF] &lt;&lt; 32
| TABLE16[(kmer &gt;&gt; 32) &amp; 0xFFFF] &lt;&lt; 16
| TABLE16[(kmer &gt;&gt; 48) &amp; 0xFFFF]
return raw &lt;&lt; (64 - 2*k)
</code></pre></div>
</div>
<p>The <strong>canonical form</strong> is the lexicographic minimum of the kmer and its reverse complement:</p>
<div class="highlight"><pre><span></span><code>canonical(kmer) = min(kmer, revcomp(kmer))
</code></pre></div>
<p>This halves the kmer space and ensures strand-independent counting.</p>
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