Elimination of Correlation in Random Codes for Arbitrarily Varying Channels

The author determines for arbitrarily varying channels a) the average error capacity and b) the maximal error capacity in case of randomized encoding. A formula for the average error capacity in case of randomized encoding was announced several years ago by Dobrushin ([3]). Under a mild regularity condition this formula turns out to be valid and follows as consequence from either a) or b). Since several articles have been written on this subject we begin right away with the mathematical notions needed. The reader not sufficiently familiar with the concepts used will find some heuristic explanations in the last Section. Let 3~ and gO be finite sets, which serve as input and output alphabets of the channels described below. Let S be an arbitrary set, and let ~={w(. I. Is): s~S} be a set of stochastic 13~1 x Igol-matrices. For every s"=(sl, ...,sn)eS"=[Is we 1 define transmission probabilities P(-I. Is n) by P(y'lx"ls")= ~I w(ytJx~lst) t=l n for all x"=(xl ..... x.)e~"=I-[~, 1 Y"=Yl .. Set ~n={p(. l" Is"): s"~Sn}. We call the sequence (g")2=1 an arbitrarily varying channel (AVC) and denote it by 96.