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For the class of mixed channels decomposed into stationary memorylesschannels, single-letter characterizations of the $\varepsilon$-capacity havenot been known except for restricted classes of channels such as the regulardecomposable channel introduced by Winkelbauer. This paper gives single-lettercharacterizations of $\varepsilon$-capacity for mixed channels decomposed intoat most countably many memoryless channels with a finite input alphabet and ageneral output alphabet with/without cost constraints. It is shown that a givencharacterization reduces to the one for the channel capacity given by Ahlswedewhen $\varepsilon$ is zero. In the proof of the coding theorem, the metaconverse bound, originally given by Polyanskiy, Poor and Verd\'u, isparticularized for the mixed channel decomposed into general componentchannels.

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