A coding theorem and converse of Kadota and Wyner revisited

A coding theorem and converse are proved for abstract channels with time structure that contain continuous-time continuous-valued channels and the result by Kadota and Wyner from 1972 as special cases. As main contribution the coding theorem is proved for a significantly weaker condition on the channel output memory and without imposing extra measurability requirements to the channel. These improvements are achieved by introducing a suitable characterization of information rate capacity. It is shown that for Gaussian channels the previously used ψ-mixing condition is equivalent to finite output memory demonstrating that it excludes important channel models. An operational perspective is taken and an abstract framework is established, which allows to treat discrete- and continuous-time channels with (possibly infinite) memory and arbitrary alphabets simultaneously in a unified way.