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Information Spectrum Methods for $\varepsilon$-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint — arXiv:2609.18352

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.18352
License (as archived): CC0-1.0
Archived: 2026-10-15T16:14:04.967Z
SHA-256 of the archived text: 32288b07b0bbcc94d43e48bcac8f4b2fe99389e6ef6cbd0b97396722dba3c1b6
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How to cite

Information Spectrum Methods for $\varepsilon$-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint — arXiv:2609.18352 — arXiv (en), https://arxiv.org/abs/2609.18352 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_e8066d283f08 (Metraipolis archive dc_e8066d283f08, sha256 32288b07b0bbcc94d43e48bcac8f4b2fe99389e6ef6cbd0b97396722dba3c1b6)

BibTeX

@misc{dce8066d283f08,
  title = {Information Spectrum Methods for $varepsilon$-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint — arXiv:2609.18352},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.18352},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_e8066d283f08; sha256 32288b07b0bbcc94d43e48bcac8f4b2fe99389e6ef6cbd0b97396722dba3c1b6},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.18352. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the $\varepsilon$-capacity regions of mixed multiple-access channels (MACs) with general mixture where the channel inputs are subject to a cost constraint from the information spectrum unified perspective. We first determine the $\varepsilon$-capacity results for additive MACs. We next give a single-letterized inner bound on the $\varepsilon$-capacity region for mixed memoryless MACs, and furthermore establish a single-letterized $0$-capacity region of the mixed memoryless MAC with finite alphabets in terms of the essential infimum of mutual informations for component channels. We also show that the MAC with additive Gaussian noise satisfies the strong converse property, which is stronger than the traditional strong converse theorem. We then focus on the quasi-static fading Gaussian MAC, for which we derive the $\varepsilon$-capacity region and show that it, in the case specialized to single-users, exactly coincides with the traditional $\varepsilon$-outage capacity region, thereby providing a Shannon-theoretic operational interpretation of the latter. We further verify that the $\varepsilon$-capacity regions coincide across four scenarios of CSI availability (no-CSI, CSIR, CSIT, and CSIRT). We also demonstrate that this coincidence generally fails for mixed MACs with general (not necessarily stationary or ergodic) components, and give a counter example to prove it. Finally, we extend these results to the $K$-user quasi-static fading Gaussian MAC.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-17 in math.IT).
Categorie arXiv: Information Theory (cs.IT).
Pagina del lavoro: https://arxiv.org/abs/2609.18352 — 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 2026-10-15T15:40:33.220Z dalla pagina https://arxiv.org/catchup/math.IT/2026-09-17?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).