Generalizing the Posterior Matching Scheme to Higher Dimensions Via Optimal Transportation

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Executive Summary

This paper re-visits Shayevitz & Feder's recent 'Posterior Matching Scheme', an explicit, dynamical system encoder for communication with feedback that treats the message as a point on the [0; 1] line and achieves capacity on memory-less channels. It has two key properties that ensure that it maximizes mutual information at each step: the encoder sequentially hands the decoder what is missing; and the next input has the desired statistics. Motivated by brain-machine interface applications and multi-antenna communications, the authors consider developing dynamical system feedback encoders for scenarios when the message point lies in higher dimensions.

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