Channels That Die

TL;DR

This paper investigates the fundamental limits of communicating over channels that can fail randomly, showing that reliable communication is impossible with arbitrarily small error, and optimizing transmission strategies within these constraints.

Contribution

It introduces a framework for analyzing channels that fail randomly, providing optimal transmission sequences and showing that feedback does not enhance performance.

Findings

Reliable communication with arbitrarily small error is impossible.

Optimal blocklength sequences maximize transmission volume.

Channel state feedback does not improve performance.

Abstract

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.