Block coding for discrete stationaryd-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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d̄</tex> -continuous channel the effect of the "past" and "future" inputs on n successive outputs dies out asymptotically with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> as measured in a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d̄</tex> or average Hamming distance sense. This is weaker than the corresponding uotious of Pfaffeihuber, Kadota, and Wyner, who require that probabilities of all <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d̄</tex> -continuous channels, and various definitions of channel capacity are compared.