{
  "abstract": "We study peeling decoding on the binary erasure channel when redundant parity checks may be added without restriction in number, but each check is subject to a row-weight constraint. For random simple binary regular low-density parity-check (LDPC) codes, we consider the parity-check matrix formed by all nonzero dual codewords up to a prescribed weight. We show that, throughout an explicit logarithmic row-weight range, this complete family of redundant checks has the same asymptotic normalized-residual threshold as peeling with the original LDPC matrix. In the same range, with probability tending to one over the random code, it still has a linear-size stopping set that is uniquely decodable. Consequently, every parity-check representation whose peeling decoder succeeds on every uniquely decodable erasure pattern must contain checks above this logarithmic scale, and the supports of those heavier checks must collectively contain a linear number of coordinates. Thus row weight remains an asymptotic limitation even when the number and selection of redundant checks are unrestricted.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05260",
  "author_total": 1,
  "authors": [
    {
      "name": "Jianshen Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dc6ewe0nmfnj0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05260",
  "fulltext_url": null,
  "id": "dc6ewe0nmfnj0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05260",
  "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": "W7220733022",
  "pdf_url": "https://arxiv.org/pdf/2610.05260",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dc6ewe0nmfnj0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05260",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05260"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Limits of Weight-Bounded Redundant Checks for Peeling Decoding of Random Regular LDPC Codes",
  "title_text": "Limits of Weight-Bounded Redundant Checks for Peeling Decoding of Random Regular LDPC Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dc6ewe0nmfnj0",
  "venue": "arXiv",
  "versions": []
}