The capacity of a channel with arbitrarily varying channel probability functions and binary output alphabet

Abstract

Let X={1,..., a} be the "input alphabet" and Y={1,2} be the "output alphabet". Let Xt=X and Yt=Y for t=1,2,..., Xn= {Mathematical expression}Xt and Yn= {Mathematical expression}Yt. Let S be any set, C=={w(·|·|)s)|s∈S} be a set of (a×2) stochastic matrices w(·∥·|s), and St=S, t=1,..., n. For every sn=(s1,..., sn)∈ {Mathematical expression}St define P(·|·|sn)= {Mathematical expression}w(yt|xt|st) for every xn=x1, ⋯, xnεXn and every yn=(y1, ⋯, yn)εYn. Consider the channel Cn={P(·|·|)sn)|sn∈Sn} with matrices (·|·|s), varying arbitrarily from letter to letter. The authors determine the capacity of this channel when a) neither sender nor receiver knows sn, b) the sender knows sn, but the receiver does not, and c) the receiver knows sn, but the sender does not. © 1970 Springer-Verlag.