A Stochastic Control Viewpoint on 'Posterior Matching'-Style Feedback Communication Schemes

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Executive Summary

This paper re-visits Shayevitz & Feder's recent 'Posterior Matching Scheme', a deterministic, recursive, capacity achieving feedback encoding scheme for memory-less channels. The authors here consider the feedback encoder design problem from a stochastic control perspective. The state of the system is the posterior distribution of the message given current outputs of the channel. The per-trial reward is the average 'Reduction in distance' of the posterior to the target unit step function. They show that the converse to the channel coding theorem with feedback upper bounds the optimal reward, and that the posterior matching scheme is an optimal policy.

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