Information Spectrum Methods for ε-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint
Abstract
We study the ε-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 ε-capacity results for additive MACs. We next give a single-letterized inner bound on the ε-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 ε-capacity region and show that it, in the case specialized to single-users, exactly coincides with the traditional ε-outage capacity region, thereby providing a Shannon-theoretic operational interpretation of the latter. We further verify that the ε-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.
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BibTeX
@misc{han2026information,
title = {{Information Spectrum Methods for $\varepsilon$-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint}},
author = {Te Sun Han and Hideki Yagi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18352},
eprint = {2609.18352},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18352},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Information Spectrum Methods for ε-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint
AU - Te Sun Han
AU - Hideki Yagi
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.18352
UR - https://arxiv.org/abs/2609.18352
AB - We study the ε-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 ε-capacity results for additive MACs. We next give a single-letterized inner bound on the ε-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 ε-capacity region and show that it, in the case specialized to single-users, exactly coincides with the traditional ε-outage capacity region, thereby providing a Shannon-theoretic operational interpretation of the latter. We further verify that the ε-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.
ER -