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A coding theorem and converse are proved for a large class of abstractstationary channels with time structure including the result by Kadota andWyner (1972) on continuous-time real-valued channels as special cases. As maincontribution the coding theorem is proved for a significantly weaker conditionon the channel output memory - called total ergodicity w.r.t. finite alphabetblock-memoryless input sources - and under a crucial relaxation of themeasurability requirement for the channel. These improvements are achieved byintroducing a suitable characterization of information rate capacity. It isshown that the $\psi$-mixing output memory condition used by Kadota and Wyneris quite restrictive and excludes important channel models, in particular forthe class of Gaussian channels. In fact, it is proved that for Gaussian (e.g.,fading or additive noise) channels the $\psi$-mixing condition is equivalent tofinite output memory. Further, it is demonstrated that the measurabilityrequirement of Kadota and Wyner is not satisfied for relevant continuous-timechannel models such as linear filters, whereas the condition used in this paperis satisfied for these models. Moreover, a weak converse is derived for allstationary channels with time structure. Intersymbol interference as well asinput constraints are taken into account in a general and flexible way,including amplitude and average power constraints as special case. Formulatedin rigorous mathematical terms complete, explicit, and transparent proofs arepresented. As a side product a gap in the proof of Kadota and Wyner -illustrated by a counterexample - is closed by providing a corrected proof of alemma on the monotonicity of some sequence of normalized mutual informationquantities. An abstract framework is established to treat discrete- andcontinuous-time channels with memory and arbitrary alphabets in a unified way.

Coding Theorem and Converse for Abstract Channels with Time Structure and Memory