  Which communication rates can be attained over a channel whose output is an
unknown (possibly stochastic) function of the input that may vary arbitrarily
in time with no a-priori model? Following the spirit of the finite-state
compressibility of a sequence, defined by Lempel and Ziv, a "capacity" is
defined for such a channel as the highest rate achievable by a designer knowing
the particular relation that indeed exists between the input and output for all
times, yet is constrained to use a fixed finite-length block communication
scheme without feedback, i.e. use the same encoder and decoder over each block.
In the case of the modulo additive channel, where the output sequence is
obtained by modulo addition of an unknown individual sequence to the input
sequence, this capacity is upper bounded by a function of the finite state
compressibility of the noise sequence. A universal communication scheme with
feedback that attains this capacity universally, without prior knowledge of the
noise sequence, is presented.
