← 研踪 PaperTrailarXiv:2611.16653 · v1
Information Spectrum Methods for Multiple-Access Channels --Part II : $\varepsilon$-Capacity Regions in the Mixed Finite-Alphabet Case
首次提交 2026-11-12 19:30
版本更新 2026-11-12 19:30
雷达观测 2026-11-13 14:15
摘要
In a nonergodic channel such as a slowly fading link, the channel law is drawn once and held fixed for the whole codeword, and the relevant performance measure is the -capacity. We study the -capacity regions of two-user mixed multiple-access channels (MACs) with finite alphabets, additive cost constraints and an arbitrary mixing measure. The direct parts are derived from a single information spectrum formula; the converse parts use, in addition, Fano's inequality and Ahlswede's strong converse applied to each component. Without knowledge of the realized component, we prove a single-letter inner bound for every , in which one input serves all components; for it is tight, and the capacity region is given by the essential infima of the component mutual informations. We prove a single-letter outer bound, the outage region, in which each component may use its own input; it holds with or without channel state information (CSI) at either terminal, and it is the -capacity region when the encoders know the component and the parameter space is countable. Both bounds coincide, in all four CSI scenarios, for well-ordered mixed MACs, which include degradedly ordered families and mixtures with a common optimal input, such as mixed additive MACs. Without CSI the outer bound can be strictly loose, and the no-CSI -capacity region for remains open in general. Finally, we extend Ahlswede's strong converse to users with cost constraints and show that most of these results extend to -user mixed MACs.
作者备注：27 pages, 2 figures
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v1 · 2026-11-12 19:30 · 最新观测版本
Information Spectrum Methods for Multiple-Access Channels --Part II : $\varepsilon$-Capacity Regions in the Mixed Finite-Alphabet Case
In a nonergodic channel such as a slowly fading link, the channel law is drawn once and held fixed for the whole codeword, and the relevant performance measure is the -capacity. We study the -capacity regions of two-user mixed multiple-access channels (MACs) with finite alphabets, additive cost constraints and an arbitrary mixing measure. The direct parts are derived from a single information spectrum formula; the converse parts use, in addition, Fano's inequality and Ahlswede's strong converse applied to each component. Without knowledge of the realized component, we prove a single-letter inner bound for every , in which one input serves all components; for it is tight, and the capacity region is given by the essential infima of the component mutual informations. We prove a single-letter outer bound, the outage region, in which each component may use its own input; it holds with or without channel state information (CSI) at either terminal, and it is the -capacity region when the encoders know the component and the parameter space is countable. Both bounds coincide, in all four CSI scenarios, for well-ordered mixed MACs, which include degradedly ordered families and mixtures with a common optimal input, such as mixed additive MACs. Without CSI the outer bound can be strictly loose, and the no-CSI -capacity region for remains open in general. Finally, we extend Ahlswede's strong converse to users with cost constraints and show that most of these results extend to -user mixed MACs.
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