Single-Letter Characterization of Epsilon-Capacity for Mixed Memoryless Channels

Abstract

For the class of mixed channels decomposed into stationary memoryless channels, single-letter characterizations of the $\epsilon$-capacity have not been known except for restricted classes of channels such as the regular decomposable channel introduced by Winkelbauer. This paper gives single-letter characterizations of $\epsilon$-capacity for mixed channels decomposed into at most countably many memoryless channels with a finite input alphabet and a general output alphabet with/without cost constraints. It is shown that a given characterization reduces to the one for the channel capacity given by Ahlswede when $\epsilon$ is zero. In the proof of the coding theorem, the meta converse bound, originally given by Polyanskiy, Poor and Verdú, is particularized for the mixed channel decomposed into general component channels.

This is an extended version of the paper submitted to the 2014 IEEE International Symposium on Information Theory (ISIT2014)