Channels with Arbitrarily Varying Channel Probability Functions in the Presence of Noiseless Feedback

In this article we study a channel with arbitrarily varying channel probability functions in the presence of a noiseless feedback channel (a. v. ch. f.). We determine its capacity by proving a coding theorem and its strong converse. Our proof of the coding theorem is constructive; we give explicitly a coding scheme which performs at any rate below the capacity with an arbitrarily small decoding error probability. The proof makes use of a new method (I l l ) to prove the coding theorem for discrete memoryless channels with noiseless feedback (d.m.c.f.). It was emphasized in [13 that the method is not based on random coding or maximal coding ideas, and it is this fact that makes it particularly suited for proving coding theorems for certain systems of channels with noiseless feedback. As a consequence of our results we obtain a formula for the zero-error capacity of a d. m. c.f., which was conjectured by Shannon ([8], p. 19).