Single-letter characterization of epsilon-capacity for mixed memoryless channels

For the class of mixed channels decomposed into stationary memoryless channels, single-letter characterizations of the ε-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 ε-capacity for mixed channels decomposed into at most countably many memoryless channels with a finite input alphabet with/without cost constraints. It is shown that the given characterization reduces to the one for the channel capacity given by Ahlswede when ε is zero. Some properties of the function of the ε-capacity are analyzed.