Universal Communication over Arbitrarily Varying Channels

Abstract

We consider the problem of universally communicating over an unknown and arbitrarily varying channel, using feedback. The focus of this paper is on determining the input behavior, and specifically, a prior distribution which is used to randomly generate the codebook. We pose the problem of setting the prior as a sequential universal prediction problem, that attempts to approach a given target rate, which depends on the unknown channel sequence. The main result is that, for a channel comprised of an unknown, arbitrary sequence of memoryless channels, there is a system using feedback and common randomness that asymptotically attains, with high probability, the capacity of the time-averaged channel, universally for every sequence of channels. While no prior knowledge of the channel sequence is assumed, the rate achieved meets or exceeds the traditional arbitrarily varying channel (AVC) capacity for every memoryless AVC defined over the same alphabets, and therefore the system universally attains the random code AVC capacity, without knowledge of the AVC parameters. The system we present combines rateless coding with a universal prediction scheme for the prior. We present rough upper bounds on the rates that can be achieved in this setting and lower bounds for the redundancies.