Rate-Distortion-Perception Function of Bernoulli Vector Sources

TL;DR

This paper characterizes the rate-distortion-perception function for Bernoulli vector sources, providing an exact solution that balances compression efficiency, distortion, and perceptual similarity, with extensions to graph sources.

Contribution

It offers the first exact characterization of the RDP function for Bernoulli vector sources with Hamming distortion and perception constraints, including a partitioning of the parameter space.

Findings

Partition of (D,P) space into three regions with similar optimal strategies

Explicit formulas for the RDP function in each region

Extension of the RDP framework to graph sources and Erdős-Rényi models

Abstract

In this paper, we consider the rate-distortion-perception (RDP) trade-off for the lossy compression of a Bernoulli vector source, which is a finite collection of independent binary random variables. The RDP function quantifies in a way the efficient compression of a source when we impose a distortion constraint that limits the dissimilarity between the source and the reconstruction and a perception constraint that restricts the distributional discrepancy of the source and the reconstruction. In this work, we obtain an exact characterization of the RDP function of a Bernoulli vector source with the Hamming distortion function and a single-letter perception function that measures the closeness of the distributions of the components of the source. The solution can be described by partitioning the set of distortion and perception levels $(D,P)$ into three regions, where in each region the optimal distortion and perception levels we allot to the components have a similar nature. Finally, we introduce the RDP function for graph sources and apply our result to the Erd\H{o}s-R\'enyi graph model.