Prediction of priors for communication over arbitrarily varying channels

Abstract

We consider the problem of communicating over an unknown and arbitrarily varying channel, using feedback. This paper focuses on the problem of determining the input behavior, or more specifically, a prior which is used to randomly generate a codebook. We pose the problem of setting the prior as a sequential universal prediction problem using information theoretic abstractions of the communication channel. For the case where the channel is block-wise constant, we show it is possible to asymptotically approach the best rate that can be attained by any system using a fixed prior. For the case where the channel may change on each symbol, we combine a rateless coding scheme with a prior predictor and asymptotically approach the capacity of the average channel universally for every sequence of channels.