BLOCK CODING FOR DISCRETE STATIONARY DBAR-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 d-continuous channel the effect of the “past” and “future” inputs on n successive outputs dies out asymptotically with n as measured in a d or average Hamming distance sense. This is weaker than the corresponding notions of Pfaffelhuber, Kadota, and Wyner, who require that probabilities of all n-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 d-continuous channels, and various definitions of channel capacity are compared. © 1979 IEEE