← 研踪 PaperTrailarXiv:2609.18352 · v3
Information Spectrum Methods for Multiple-Access Channels--Part I: $\varepsilon$-Capacity Regions in the Mixed Gaussian Case
多址信道的信息谱方法——第一部分：混合高斯情形下的 ε-容量区域
首次提交 2026-09-16 17:13
版本更新 2026-11-13 01:57
雷达观测 2026-11-13 14:15
摘要
We study the ε-capacity regions of mixed multiple-access channels (MACs) with general mixture and cost constraints by the information spectrum method. The starting point is a general formula for the ε-capacity region of general MACs with cost constraint, together with the random-coding and converse lemmas from which it is derived. For the quasi-static fading Gaussian MAC, with random fading coefficients and noise variance, we show that the ε-capacity region is the ε-outage capacity region, which gives the latter a Shannon-theoretic operational meaning. The direct part follows from the general formula, and the converse part from the strong converse property of the Gaussian MAC, which is stronger than the ε-strong converse, applied to each component. The ε-capacity regions coincide in all four scenarios of availability of channel state information (CSI), and the results extend to K users. With CSI at both terminals, variable-rate coding enlarges the 0-capacity region to the polymatroid whose rank function is the average of those of the components. For mixed MACs with general components and a countable parameter space, CSI at the receiver alone never enlarges the ε-capacity region, and the region with CSI at the transmitters is given by an information spectrum formula; unlike the Gaussian case, the regions with and without CSI at the transmitters may differ. For uncountable parameter spaces, only the formula for the region with CSI at both terminals survives in general. Parts II and III treat finite-alphabet mixed MACs and the strong converse for the K-user Gaussian MAC, respectively.
作者备注：30 pages, 2 figures
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v3 · 2026-11-13 01:57 · 最新观测版本
Information Spectrum Methods for Multiple-Access Channels--Part I: $\varepsilon$-Capacity Regions in the Mixed Gaussian Case
We study the ε-capacity regions of mixed multiple-access channels (MACs) with general mixture and cost constraints by the information spectrum method. The starting point is a general formula for the ε-capacity region of general MACs with cost constraint, together with the random-coding and converse lemmas from which it is derived. For the quasi-static fading Gaussian MAC, with random fading coefficients and noise variance, we show that the ε-capacity region is the ε-outage capacity region, which gives the latter a Shannon-theoretic operational meaning. The direct part follows from the general formula, and the converse part from the strong converse property of the Gaussian MAC, which is stronger than the ε-strong converse, applied to each component. The ε-capacity regions coincide in all four scenarios of availability of channel state information (CSI), and the results extend to K users. With CSI at both terminals, variable-rate coding enlarges the 0-capacity region to the polymatroid whose rank function is the average of those of the components. For mixed MACs with general components and a countable parameter space, CSI at the receiver alone never enlarges the ε-capacity region, and the region with CSI at the transmitters is given by an information spectrum formula; unlike the Gaussian case, the regions with and without CSI at the transmitters may differ. For uncountable parameter spaces, only the formula for the region with CSI at both terminals survives in general. Parts II and III treat finite-alphabet mixed MACs and the strong converse for the K-user Gaussian MAC, respectively.
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