Problem
Research questions and friction points this paper is trying to address.
ε-capacity
mixed multiple-access channels
cost constraint
information spectrum method
fading Gaussian MAC
Information Spectrum Methods for $\varepsilon$-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint
🤖 AI Summary
本文研究了混合多址接入信道在成本约束下的ε-容量问题，使用信息谱方法给出了单字母化内界，并验证了不同信道状态信息场景下的ε-容量区域一致性。
📝 Abstract
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. 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 Gaussian MAC with additive Gaussian noise satisfies the strong converse property, which is stronger than the traditional strong converse theorem, via a simple proof based on the information spectrum method that does not require the well-known ``wringing'' technique. 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, via the information spectrum method, 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
information spectrum method
ε-capacity region
mixed multiple-access channels
strong converse property
quasi-static fading Gaussian MAC
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