Rate-Distortion-Classification Representation Theory for Bernoulli Sources
Provides theoretical foundations for task-oriented lossy compression in a specific setting, but is incremental as it extends known RDC theory to Bernoulli sources.
This paper derives closed-form characterizations of rate-distortion-classification (RDC) tradeoffs for Bernoulli sources with Hamming distortion and binary symmetric classification, and provides bounds on the rate penalty for universal encoders supporting multiple operating points.
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.