A Communication Optimal Transport Approach to the Computation of Rate Distortion Functions

TL;DR

This paper introduces Communication Optimal Transport (CommOT), a novel framework that leverages optimal transport theory to efficiently compute rate distortion functions in information theory.

Contribution

The paper presents a new OT-based framework for RD function computation, incorporating slackness variables and solving via Sinkhorn algorithm, improving efficiency and accuracy.

Findings

Efficient computation of RD functions demonstrated.

CommOT framework outperforms traditional methods in accuracy.

Numerical experiments confirm the method's effectiveness.

Abstract

In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in communication theory can be viewed as the transport plan and the regularized objective function in the optimal transport (OT) model. However, unlike in classical OT problems, the RD function only possesses one-side marginal distribution. Hence, to maintain the OT structure, we introduce slackness variables to fulfill the other-side marginal distribution and then propose a general framework (CommOT) for the RD function. The CommOT model is solved via the alternating optimization technique and the well-known Sinkhorn algorithm. In particular, the expected distortion threshold can be converted into finding the unique root of a one-dimensional monotonic function with only a few steps. Numerical experiments show that our proposed framework (CommOT) for solving the RD function with given distortion threshold is efficient and accurate.