{
  "abstract": "We prove a capacity criterion for fixed-degree spatially coupled MacKay--Neal codes on additive symmetric Markov noise. The noise bit flips with probability $p$, so the channel has one parameter and capacity $1-h_2(p)$. For every integer $\\ell\\geq4$ with $3/\\ell<1-h_2(p)$, matched finite-window BCJR and sum-product decoding admit code sequences, possibly depending on $p$, with actual rate tending to $3/\\ell$ and vanishing average information-bit error. The proof parallels the GEC-to-BEC argument: a conditional-entropy correction transfers BMS fixed-point positivity to the channel with memory. The correction also covers a capacity deficit of the effective BMS channel. A two-state posterior contraction supplies the additional derivative bound needed for threshold saturation. The result uses the cited BMS positivity theorem, with an analytic proof for $\\ell\\geq33$ and exact interval certificates for $4\\leq\\ell\\leq32$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00227",
  "author_total": 1,
  "authors": [
    {
      "name": "Kenta Kasai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sytqqev9tyd3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00227",
  "fulltext_url": null,
  "id": "0sytqqev9tyd3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00227",
  "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",
      "1705|Error Correcting Code Techniques"
    ]
  ],
  "openalex": "W7215878393",
  "pdf_url": "https://arxiv.org/pdf/2610.00227",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0sytqqev9tyd3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00227",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00227"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Spatially Coupled MacKay-Neal Codes on Symmetric Markov Noise: A Reduction to BMS Channels",
  "title_text": "Spatially Coupled MacKay-Neal Codes on Symmetric Markov Noise: A Reduction to BMS Channels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/0sytqqev9tyd3",
  "venue": "arXiv",
  "versions": []
}