On a Relation Between the Rate-Distortion Function and Optimal Transport

TL;DR

This paper reveals a fundamental connection between rate-distortion theory and optimal transport, showing they can be unified through entropic OT distances, with numerical verification of the equivalence and related quantization results.

Contribution

It establishes a novel theoretical link between rate-distortion functions and entropic optimal transport, enabling unified solutions via OT solvers.

Findings

Rate-distortion function equals an extremal entropic OT distance.

Numerical verification confirms the theoretical equivalence.

Unifies scalar quantization and rate-distortion computation using OT methods.

Abstract

We discuss a relationship between rate-distortion and optimal transport (OT) theory, even though they seem to be unrelated at first glance. In particular, we show that a function defined via an extremal entropic OT distance is equivalent to the rate-distortion function. We numerically verify this result as well as previous results that connect the Monge and Kantorovich problems to optimal scalar quantization. Thus, we unify solving scalar quantization and rate-distortion functions in an alternative fashion by using their respective optimal transport solvers.