信息谱方法用于带成本约束的混合多址信道理论中的 $\varepsilon$-容量问题
Information Spectrum Methods for $\varepsilon$-Capacity Problems in the Theory of Mixed Multiple-Access Channels with Cost Constraint
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中文总结 AI 辅助
本文用信息谱方法研究带成本约束的混合多址信道的 $\varepsilon$-容量，给出内界、高斯MAC强逆性质及准静态衰落高斯MAC的容量区域，并验证CSI场景下的一致性。
中文摘要 AI 辅助
我们研究了具有一般混合的混合多址信道（MACs）的 $\varepsilon$-容量区域，其中信道输入受成本约束。我们首先确定了加性MAC的 $\varepsilon$-容量结果。接下来，我们给出了混合无记忆MAC的 $\varepsilon$-容量区域的单字母化内界，并进一步建立了具有有限字母表的混合无记忆MAC的单字母化 $0$-容量区域，该区域以分量信道的互信息的本质下确界表示。我们还证明了具有加性高斯噪声的高斯MAC满足强逆性质，这比传统的强逆定理更强，通过基于信息谱方法的简单证明，该方法不需要众所周知的“拧干”技术。然后我们专注于准静态衰落高斯MAC，为此我们推导了 $\varepsilon$-容量区域，并表明在单用户特例中，它恰好与传统 $\varepsilon$-中断容量区域一致，从而为后者提供了香农理论上的操作解释。我们进一步通过信息谱方法验证，在四种CSI可用性场景（无CSI、CSIR、CSIT和CSIRT）下，$\varepsilon$-容量区域是一致的。我们还证明了这种一致性对于具有一般（不一定是平稳或遍历的）分量的混合MAC通常不成立，并给出了一个反例来证明这一点。最后，我们将这些结果扩展到 $K$-用户准静态衰落高斯MAC。
英文摘要
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.
发表机构
- The University of Electro-Communications（电气通信大学）
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