The Discrete Finite-Memory Channel

Abstract

We begin this chapter with a desription of the general discrete channel. The term “discrete” means that both input and output alphabets have a finite number of elements. For the sake of simplicity and without essential loss of generality we take both these alphabets to be {1, ... , a}. This will lighten somewhat the heavy burden of definitions and notation. The application of the theorems to cases where the alphabets have different numbers of elements will be obvious and will be made freely. (See also Chapter 3, Remark 10.) It is hoped that this manner of proceeding will make things less ponderous. Unless the contrary is explicitly stated the channels involved will have a single c.p.f., unlike, for example, the compound channels of Chapter 4.