{
  "abstract": "This work studies non-linear function computation broadcast (NFCB), in which a sender with access to $N$ datasets $(X_1,\\dots,X_N)$ broadcasts a common message to $K$ users, each possessing side information and requesting a function of the datasets. The goal is to minimize the rate required for asymptotically lossless recovery of all demands. We introduce a broadcast graph that jointly captures the source distribution, side information, and demanded functions. Using Körner's characteristic-graph framework, we develop an achievable scheme for arbitrary $K$, general source distributions, and general finite-field demands, including linear, non-separable, and non-linear functions, without restricting the encoding or decoding operations to be linear. We also present a side-information-assisted independent-set scheme and characterize the optimal graph-based achievable rate for compatible functions. For the converse, we derive a multi-letter response-profile bound that strengthens a basic side-information converse, zero-error and asymptotically lossless clique-entropy bounds based on the operational block broadcast graph, and a genie-aided lower bound. For binary NFCB with $N=K$ and side information $X_i$ at user $i$, we characterize the optimal rate in several special cases and bound the worst-case and average additive gaps between the proposed achievable rate and the genie-aided converse for $K=3$ and $K=4$. Finally, three-user examples with Boolean and linear demands illustrate the proposed bounds and show that non-linear encoding can strictly outperform the best scalar and vector linear schemes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08202",
  "author_total": 3,
  "authors": [
    {
      "name": "Derya Malak"
    },
    {
      "name": "Vijith Kumar K. P."
    },
    {
      "name": "M. Reza Deylam Salehi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1atqynpgs520n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08202",
  "fulltext_url": null,
  "id": "1atqynpgs520n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08202",
  "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|Cooperative Communication and Network Coding"
    ]
  ],
  "openalex": "W7220958879",
  "pdf_url": "https://arxiv.org/pdf/2610.08202",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1atqynpgs520n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08202",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08202"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Graph-Theoretic Bounds for Non-Linear Function Computation Broadcast",
  "title_text": "Graph-Theoretic Bounds for Non-Linear Function Computation Broadcast",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/1atqynpgs520n",
  "venue": "arXiv",
  "versions": []
}