{
  "abstract": "Within the Thompson VLSI model, the first energy optimal decoding schemes (up to polylogarithmic factors) that also reach clock cycle lower bounds are constructed. Let $N$ be block length. Then, there is an exponential error scaling function and a binary symmetric channel, such that for all $f(N)$ that scales to zero more slowly than this, there is a decoding scheme for this channel with error probability that scales as $O(f(N))$ that has number of clock cycles $T\\le O(\\sqrt{-\\log(f(N)})\\text{polylog}(N))$ and energy $E\\le O(N\\sqrt{-\\log(f(N))}\\text{polylog}(N))$. This matches fundamental lower bounds up to polylogarithmic factors. The technique uses expander-graph based LDPC codes, a mesh network architecture, and a parallelization technique. The key technical result needed for this is a lemma in graph theory. This lemma is used to show that communication graphs of bounded node degree can be routed through two- and three-dimensional mesh networks without overflowing the memory of any mesh node. Upper bounds are also extended to three dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07336",
  "author_total": 1,
  "authors": [
    {
      "name": "Christopher Blake"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b8p6nkf4wgbt6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07336",
  "fulltext_url": null,
  "id": "b8p6nkf4wgbt6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07336",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07336",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b8p6nkf4wgbt6.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07336",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07336"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Energy-Time Optimal Decoding Using Expander-Graph LDPC Codes and Mesh Network Architecture",
  "title_text": "Energy-Time Optimal Decoding Using Expander-Graph LDPC Codes and Mesh Network Architecture",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/b8p6nkf4wgbt6",
  "venue": "arXiv",
  "versions": []
}