  We consider the problem of communicating over a channel for which no
mathematical model is specified, and the achievable rates are determined as a
function of the channel input and output sequences known a-posteriori, without
assuming any a-priori relation between them. In a previous paper we have shown
that the empirical mutual information between the input and output sequences is
achievable without specifying the channel model, by using feedback and common
randomness, and a similar result for real-valued input and output alphabets. In
this paper, we present a unifying framework which includes the two previous
results as particular cases. We characterize the region of rate functions which
are achievable, and show that asymptotically the rate function is equivalent to
a conditional distribution of the channel input given the output. We present a
scheme that achieves these rates with asymptotically vanishing overheads.
