Empirical and Strong Coordination via Soft Covering with Polar Codes

TL;DR

This paper introduces polar codes for empirical and strong coordination in two-node networks, achieving capacity regions with explicit low-complexity schemes that improve upon previous methods by handling non-uniform distributions and reducing randomness needs.

Contribution

It presents novel polar coding schemes for coordination that work with arbitrary distributions and require less randomness, expanding the applicability of polar codes in network coordination.

Findings

Achieves capacity regions for empirical and strong coordination.

Provides explicit low-complexity coding schemes based on polar codes.

Improves upon previous polar coding schemes by handling non-uniform distributions.

Abstract

We design polar codes for empirical coordination and strong coordination in two-node networks. Our constructions hinge on the fact that polar codes enable explicit low-complexity schemes for soft covering. We leverage this property to propose explicit and low-complexity coding schemes that achieve the capacity regions of both empirical coordination and strong coordination for sequences of actions taking value in an alphabet of prime cardinality. Our results improve previously known polar coding schemes, which (i) were restricted to uniform distributions and to actions obtained via binary symmetric channels for strong coordination, (ii) required a non-negligible amount of common randomness for empirical coordination, and (iii) assumed that the simulation of discrete memoryless channels could be perfectly implemented. As a by-product of our results, we obtain a polar coding scheme that achieves channel resolvability for an arbitrary discrete memoryless channel whose input alphabet has prime cardinality.