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A Necessary Condition for Reliable Communication With Feedback Based Upon Lyapunov Exponents of Dynamical Systems

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Executive Summary

In this paper, the authors use control theoretic techniques to provide a new perspective for understanding what makes a channel coding scheme good. They show that for a class of memoryless feedback channels, the Lyapunov Exponent of the transmission function - when it exists - is fundamentally linked to the maximum rate which the scheme can attain. More generally, they can upper-bound the set of achievable rates for a given encoding scheme by considering a generalization of the Lyapunov Exponent of the transmission function. By approaching the problem from a dynamical systems perspective, they hope to provide the intuition to motivate the evaluation and design of new coding schemes.

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