Block coding for discrete stationary -continuous noisy channels

A new class of discrete stationary noisy channels with memory and anticipation termed d-continuous channels is introduced and is shown to include all stationary discrete channels for which coding theorems exist. Roughly speaking, in a -continuous channel the effect of the "past" and "future" inputs on n successive outputs dies out asymptotically with as measured in a or average Hamming distance sense. This is weaker than the corresponding uotious of Pfaffeihuber, Kadota, and Wyner, who require that probabilities of all -tuples be close; that is, closeness in a variational or distribution sense. General block channel coding and block joint source and channel coding theorems are proved for stationary -continuous channels, and various definitions of channel capacity are compared.