  Given the possibility of communication systems failing catastrophically, we
investigate limits to communicating over channels that fail at random times.
These channels are finite-state semi-Markov channels. We show that
communication with arbitrarily small probability of error is not possible.
Making use of results in finite blocklength channel coding, we determine
sequences of blocklengths that optimize transmission volume communicated at
fixed maximum message error probabilities. We provide a partial ordering of
communication channels. A dynamic programming formulation is used to show the
structural result that channel state feedback does not improve performance.
