Information Spectrum Methods for Multiple-Access Channels --Part II : $\varepsilon$-Capacity Regions in the Mixed Finite-Alphabet Case
Te Sun Han, Hideki Yagi
原文摘要
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 $\varepsilon$-capacity. We study the $\varepsilon$-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 $0\le\varepsilon<1$, in which one input serves all components; for $\varepsilon=0$ 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 $\varepsilon$-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 $\varepsilon$-capacity region for $0<\varepsilon<1$ remains open in general. Finally, we extend Ahlswede's strong converse to $K$ users with cost constraints and show that most of these results extend to $K$-user mixed MACs.
cs.IT