{
  "abstract": "Task-oriented communication conveys information that is necessary for downstream tasks. For binary decision tasks, this paradigm is information-theoretically formalized by Boolean function computation (BFC) via channels, where the receiver aims to determine the value of a function unknown to the transmitter. In this paper, we devise a practical code construction for the BFC problem based on a Reed-Solomon code. For noiseless binary channels, we derive finite-blocklength worst-case error bounds. By defining a rate function that captures how supported message length scales with channel uses, we characterize the rate-reliability tradeoff for different Boolean function families. With respect to this rate function, the proposed construction achieves an asymptotic computation rate of $1/2$. We further extend this construction to noisy channels by packing multiple BFC tasks into a single block and concatenating them with a conventional channel code. The corresponding finite-blocklength guarantees are expressed in terms of effective channel uses per function evaluation. With a channel code rate $R_c$, this construction achieves an asymptotic computation rate of $R_c/2$, yielding $C/2$ when capacity-achieving channel codes are employed. Numerical results illustrate the derived bounds and demonstrate substantial performance gains over conventional transmission. As examples, the proposed scheme achieves SNR coding gains of approximately $3.4$ and $6.4$ dB at an average task error probability of $10^{-5}$ for the exact-weight and rank-test tasks, respectively.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01228",
  "author_total": 3,
  "authors": [
    {
      "name": "Yangshuo He"
    },
    {
      "name": "Guanding Yu"
    },
    {
      "name": "Jingge Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0gdje3e5ar0t6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01228",
  "fulltext_url": null,
  "id": "0gdje3e5ar0t6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01228",
  "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": "W7216171498",
  "pdf_url": "https://arxiv.org/pdf/2610.01228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0gdje3e5ar0t6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.01228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Task-Oriented Boolean Function Computation: Practical Code Constructions",
  "title_text": "Task-Oriented Boolean Function Computation: Practical Code Constructions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/0gdje3e5ar0t6",
  "venue": "arXiv",
  "versions": []
}