  Consider communication over a channel whose probabilistic model is completely
unknown vector-wise and is not assumed to be stationary. Communication over
such channels is challenging because knowing the past does not indicate
anything about the future. The existence of reliable feedback and common
randomness is assumed. In a previous paper it was shown that the Shannon
capacity cannot be attained, in general, if the channel is not known. An
alternative notion of "capacity" was defined, as the maximum rate of reliable
communication by any block-coding system used over consecutive blocks. This
rate was shown to be achievable for the modulo-additive channel with an
individual, unknown noise sequence, and not achievable for some channels with
memory. In this paper this "capacity" is shown to be achievable for general
channel models possibly including memory, as long as this memory fades with
time. In other words, there exists a system with feedback and common randomness
that, without knowledge of the channel, asymptotically performs as well as any
block code, which may be designed knowing the channel. For non-fading memory
channels a weaker type of "capacity" is shown to be achievable.
