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Cache-Aided Linear Function Computation — arXiv:2610.20323

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.20323
License (as archived): CC0-1.0
Archived: 2026-10-15T14:36:18.043Z
SHA-256 of the archived text: c9f30637e6d41b399d426264ed32ee0aa66d189a351289a1cb17e84756a3ff59
Stable URL of this page: https://metraipolis.com/documento/dc_a8807cedbb45

How to cite

Cache-Aided Linear Function Computation — arXiv:2610.20323 — arXiv (en), https://arxiv.org/abs/2610.20323 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_a8807cedbb45 (Metraipolis archive dc_a8807cedbb45, sha256 c9f30637e6d41b399d426264ed32ee0aa66d189a351289a1cb17e84756a3ff59)

BibTeX

@misc{dca8807cedbb45,
  title = {Cache-Aided Linear Function Computation — arXiv:2610.20323},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.20323},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_a8807cedbb45; sha256 c9f30637e6d41b399d426264ed32ee0aa66d189a351289a1cb17e84756a3ff59},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.20323. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study cache-aided linear computation in distributed systems where each source generates and stores its own data. An external receiver requests a linear combination of these data, and the sources use information cached before the request is known to reduce the communication needed to recover the requested result. In our model, each of the $N$ sources stores its own independent file over a finite field and has an additional cache of normalized size $M$. The receiver must recover any requested linear combination with zero error from the messages sent by the sources over separate noiseless links. We establish a lower bound on the worst-case communication rate over any finite field by analyzing several requests under the same cache placement. This bound determines the optimal rate when no additional cache is available. For binary files, we propose parity-aided placement (PAP), a coded-placement scheme that combines cached parities with uncoded symbols. For every $N\geq3$, we characterize its communication rate for each request and optimize its placement parameters to obtain a closed-form worst-case rate. The resulting achievable rate meets the lower bound for $0\leq M\leq1/(2N-1)$ and $M\geq(N-1)/N$, establishing the optimal memory--rate tradeoff in these two ranges.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2610.20323 — 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 2026-10-15T13:57:05.403Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).