A New Method for Employing Feedback to Improve Coding Performance

TL;DR

This paper introduces timid/bold feedback coding for discrete memoryless channels, showing it improves second-order rates for certain channels and characterizing when feedback is beneficial.

Contribution

It presents a novel feedback mechanism, characterizes the class of channels where feedback improves coding rates, and relates feedback codes to controlled diffusions.

Findings

Feedback improves second-order rates for compound-dispersion channels.

Feedback does not improve rates for non-compound dispersion or very noisy channels.

Provides an upper bound on the second-order coding rate for certain channels.

Abstract

We introduce a novel mechanism, called timid/bold coding, by which feedback can be used to improve coding performance. For a certain class of DMCs, called compound-dispersion channels, we show that timid/bold coding allows for an improved second-order coding rate compared with coding without feedback. For DMCs that are not compound dispersion, we show that feedback does not improve the second-order coding rate. Thus we completely determine the class of DMCs for which feedback improves the second-order coding rate. An upper bound on the second-order coding rate is provided for compound-dispersion DMCs. We also show that feedback does not improve the second-order coding rate for very noisy DMCs. The main results are obtained by relating feedback codes to certain controlled diffusions.