{
  "abstract": "We prove that the capacity of the binary deletion channel satisfies $C(d)\\le (1-d)/4$ for every $13/20\\le d<1$. The proof describes the output from right to left, using a six-bit context to assign a description length. We bound the increase in expected description length minus output entropy when one input bit is added. A relative-entropy identity reduces this bound to finitely many linear inequalities. A potential on input windows of length 26 makes the inequalities telescope, giving a bound for every input word. Deletion composition extends the result from $d=13/20$ to all larger deletion probabilities. We also obtain finite-block bounds on mutual information and decoding error, with explicit $O(\\log n/n)$ corrections. The finite certificate is checked using exact integer arithmetic, and the proof is formalized end to end in Lean.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13351",
  "author_total": 1,
  "authors": [
    {
      "name": "Özgür Soysal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvrzch5thmyw2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13351",
  "fulltext_url": null,
  "id": "dvrzch5thmyw2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13351",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1705|Error Correcting Code Techniques"
    ]
  ],
  "openalex": "W7213232811",
  "pdf_url": "https://arxiv.org/pdf/2609.13351",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvrzch5thmyw2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.13351",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13351"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "A New Upper Bound on the Binary Deletion Channel Capacity",
  "title_text": "A New Upper Bound on the Binary Deletion Channel Capacity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/dvrzch5thmyw2",
  "venue": "arXiv",
  "versions": []
}