A direct proof of the coding theorem for discrete sources with memory

In this paper we provide an alternate method of proving the existence theorem for the coding of discrete stationary ergodic sources subject to a fidelity constraint. This method differs from previously published proofs for sources with memory in that a random coding argument is obtained directly for the coding of source
n
-tuples. The main advantage of the technique employed in this paper is that it can easily be extended to yield the basis for the proof of the coding theorem for more general sources (e.g., nonergodic) and for sources with unknown parameters.