{
  "abstract": "We study the approximate channel simulation problem in the normal approximation regime. Our starting point is the fact established by Cao et al.~\\cite{Cao_channel_simulation}, that the minimal codebook size $M_ε^*(W)$ for a fixed error tolerance $ε>0$ is closely related to the $ε$-smooth channel max-information, $I_{\\max}^ε(W)$. Using this, we refine earlier large-blocklength approximations to $M_ε^*(W^{\\otimes n})$ for discrete memoryless channels. Specifically, we provide tight third-order expansions for Gallager-symmetric channels and demonstrate that the third-order term is channel-dependent. As in corresponding channel coding expansions, we identify a substantial rate gap between singular and nonsingular channels. Notably, the direction of this gap is reversed relative to channel coding: The third-order term is $-\\frac{1}{2}\\log n$ for singular channels but $O(\\log\\log n)$ for nonsingular channels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15877",
  "author_total": 3,
  "authors": [
    {
      "name": "Valentinian Lungu"
    },
    {
      "name": "Aaron B. Wagner"
    },
    {
      "name": "Ioannis Kontoyiannis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ensykgzsatm7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15877",
  "fulltext_url": null,
  "id": "2ensykgzsatm7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15877",
  "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",
      "1705|Error Correcting Code Techniques"
    ]
  ],
  "openalex": "W7221765359",
  "pdf_url": "https://arxiv.org/pdf/2610.15877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ensykgzsatm7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15877"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Fine asymptotics for approximate simulation of symmetric channels",
  "title_text": "Fine asymptotics for approximate simulation of symmetric channels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/2ensykgzsatm7",
  "venue": "arXiv",
  "versions": []
}