Channels that die

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 block-length channel coding, we determine sequences of block-lengths that optimize transmission volume communicated at fixed maximum message error probabilities. A dynamic programming formulation is used to show that channel state feedback does not improve performance.