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An InformationTheoretic Characterization of Channels That Die
"... Abstract—Given the possibility of communication systems failing catastrophically, we investigate limits to communicating over channels that fail at random times. These channels are finitestate semiMarkov channels. We show that communication with arbitrarily small probability of error is not possib ..."
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Abstract—Given the possibility of communication systems failing catastrophically, we investigate limits to communicating over channels that fail at random times. These channels are finitestate semiMarkov 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. Index Terms—Channel coding, communication channels, dynamic programming, finite blocklength regime, reliability theory. “a communication channel … might be inoperative because of an amplifier failure, a broken or cut telephone wire,…” —I. M. Jacobs