Rate-Distortion-Perception Function of Bernoulli Vector Sources

2025-01-21

AI Summary

This paper investigates the rate–distortion–perception (RDP) trade-off for Bernoulli vector sources under joint Hamming distortion and single-letter perception constraints. Using tools from information theory, single-letterization, convex optimization, and KL divergence, we derive the first closed-form expression for the RDP function of this source. The (D, P)-plane is precisely partitioned into three structurally distinct regions, revealing a trichotomous nature of optimal component-wise resource allocation. Our approach transcends classical rate–distortion theory by establishing the first computable RDP benchmark for structured data models—specifically, Erdős–Rényi random graphs. Key contributions are: (1) a complete characterization of the RDP function for Bernoulli vector sources; (2) a novel paradigm for region partitioning based on component-level allocation; and (3) a substantive extension of RDP theory to structured data domains, notably graph-structured sources.

Technology Category

• Machine Learning: Information Theory
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

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 ErdH{o}s-R'enyi graph model.

Problem

• Compression Efficiency
• Distortion
• Perceptual Quality

Innovation

• Bernoulli vector compression
• RDP function
• perceptual quality optimization