{
  "abstract": "Maximum-likelihood (ML) decoding of linear block codes is NP-hard, so neural decoders are evaluated by how closely they approach it. We observe that proving a candidate optimal can be far easier than finding it, and build a decoder that does both. We cast decoding as a search over an absorbing-state discrete diffusion model, whose sequential commitment of coordinates turns generation into a tree, and run a probability beam search over it. A dual bound from a linear-programming relaxation and a distance-based test, both derived from the code, then certify per frame that the current candidate is the global ML solution; because both are theorems, certified frames incur no accuracy-computation trade-off. Across $15$ codes and five operating points we certify up to $99.9\\%$ of frames, the two tests dividing the space as their derivations predict, one strong for sparse parity-check matrices and the other for codes with a large minimum distance. Certification also behaves as a per-frame reliability signal, with $96.7$-$100\\%$ of all frame errors falling on uncertified frames. Against an exact ML reference at $5$ dB the decoder is within one standard deviation on three of the four codes where the reference is uncensored, and against four neural baselines it attains the best bit-error rate in $71$ of $75$ cells.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27805",
  "author_total": 3,
  "authors": [
    {
      "name": "Jaeho Hwang"
    },
    {
      "name": "Byung-Sun Won"
    },
    {
      "name": "Uiwon Hwang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4s803rw4v4ynk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27805",
  "fulltext_url": null,
  "id": "4s803rw4v4ynk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27805",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1705|Error Correcting Code Techniques"
    ]
  ],
  "openalex": "W7223156185",
  "pdf_url": "https://arxiv.org/pdf/2610.27805",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4s803rw4v4ynk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27805",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27805"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Certified Adaptive List Decoding for Error-Correcting Codes",
  "title_text": "Certified Adaptive List Decoding for Error-Correcting Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/4s803rw4v4ynk",
  "venue": "arXiv",
  "versions": []
}