{
  "abstract": "We prove achievability below the symmetric information rate (SIR) under block maximum a posteriori (MAP) decoding for a fixed-degree MacKay-Neal (MN) socket ensemble on the quaternary insertion-deletion-substitution channel used to model DNA reads. For every integer $\\ell\\ge4$, the $(\\ell,3,3)$ socket ensemble, with one transmitted bit fixed and an independent uniform known offset, has limiting rate $r_\\star=6/\\ell$ bits per stored nucleotide. If the joint SIR $J_t$ of a fixed number $t$ of reads under independent, uniformly distributed input nucleotides exceeds $r_\\star$, the ensemble-average full extended-word block error is $O(1/n)$, and deterministic graph-offset sequences attain the same limiting rate and message-average error bound. This result concerns the discrete rate family $6/\\ell$, not arbitrary rates approaching a given SIR. The channel permits arbitrarily many insertions and unbounded drift, with no alignment supplied to the receiver. The proof combines established MN parity and distance estimates with a strict arbitrary-candidate-list bound and a list construction that accounts for hidden output boundaries.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38440",
  "author_total": 1,
  "authors": [
    {
      "name": "Kenta Kasai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/46sp6tvns1ag8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38440",
  "fulltext_url": null,
  "id": "46sp6tvns1ag8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38440",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38440",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/46sp6tvns1ag8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38440",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38440"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "MacKay-Neal Codes for DNA Channels under Block-MAP Decoding",
  "title_text": "MacKay-Neal Codes for DNA Channels under Block-MAP Decoding",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/46sp6tvns1ag8",
  "venue": "arXiv",
  "versions": []
}