{
  "abstract": "Let $X$ be a uniform random bit string and $Y$ be obtained by flipping each bit of $X$ independently with probability $p$. Let $C$ be a random bit obtained as a function of $Y$. We show that $\\mathbf{I}(C:X)\\le \\mathbf{I}(Y_1:X)$ for all $p\\in[0,1]$, which resolves a conjecture posed by Courtade and Kumar in 2013.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05430",
  "author_total": 2,
  "authors": [
    {
      "name": "Dimiter Kramer"
    },
    {
      "name": "Mert Saglam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fe4ttek8qme88.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05430",
  "fulltext_url": null,
  "id": "fe4ttek8qme88",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05430",
  "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.CO"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05430",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fe4ttek8qme88.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.05430",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05430"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the most informative Boolean function under noise",
  "title_text": "On the most informative Boolean function under noise",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:29Z",
  "url": "https://research.draconitic.com/paper/fe4ttek8qme88",
  "venue": "arXiv",
  "versions": []
}