Rate-Distortion-Classification Representation Theory for Bernoulli Sources

TL;DR

This paper develops a theoretical framework for task-oriented lossy compression of Bernoulli sources, deriving explicit characterizations of the rate-distortion-classification tradeoffs and bounds on universal encoding rates.

Contribution

It introduces closed-form characterizations of RDC and DRC tradeoffs for Bernoulli sources and analyzes universal encoders supporting multiple operating points.

Findings

Derived closed-form RDC and DRC tradeoff characterizations.

Established bounds on the minimum rate for universal encoders.

Numerical examples illustrating achievable regions and tradeoff curves.

Abstract

We study task-oriented lossy compression through the lens of rate-distortion-classification (RDC) representations. The source is Bernoulli, the distortion measure is Hamming, and the binary classification variable is coupled to the source via a binary symmetric model. Building on the one-shot common-randomness formulation, we first derive closed-form characterizations of the one-shot RDC and the dual distortion-rate-classification (DRC) tradeoffs. We then use a representation-based viewpoint and characterize the achievable distortion-classification (DC) region induced by a fixed representation by deriving its lower boundary via a linear program. Finally, we study universal encoders that must support a family of DC operating points and derive computable lower and upper bounds on the minimum asymptotic rate required for universality, thereby yielding bounds on the corresponding rate penalty. Numerical examples are provided to illustrate the achievable regions and the resulting universal RDC/DRC curves.