  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.
