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Task-Oriented Boolean Function Computation: Practical Code Constructions — arXiv:2610.01228

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.01228
License (as archived): CC0-1.0
Archived: 2026-10-06T17:48:09.470Z
SHA-256 of the archived text: 21c3c22f193772f85cedeb5a842ad73c3cc37f998da069240b2d988ae5a26f0b
Stable URL of this page: https://metraipolis.com/documento/dc_2c4418c8a4e7

How to cite

Task-Oriented Boolean Function Computation: Practical Code Constructions — arXiv:2610.01228 — arXiv (en), https://arxiv.org/abs/2610.01228 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_2c4418c8a4e7 (Metraipolis archive dc_2c4418c8a4e7, sha256 21c3c22f193772f85cedeb5a842ad73c3cc37f998da069240b2d988ae5a26f0b)

BibTeX

@misc{dc2c4418c8a4e7,
  title = {Task-Oriented Boolean Function Computation: Practical Code Constructions — arXiv:2610.01228},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.01228},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_2c4418c8a4e7; sha256 21c3c22f193772f85cedeb5a842ad73c3cc37f998da069240b2d988ae5a26f0b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.01228. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 scaling, 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 coding scheme achieves SNR coding gains of approximately $3.4$ and $6.4$~dB for the exact-weight and rank-test tasks, respectively.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-10-02 in math.IT).
Categorie arXiv: Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2610.01228 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T16:13:30.419Z dalla pagina https://arxiv.org/catchup/math.IT/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).