Rate-Distortion-Perception Tradeoff for the Gray-Wyner Problem

2026-01-16

AI Summary

This work introduces perceptual constraints into the Gray–Wyner multiterminal source coding framework for the first time, investigating the fundamental trade-off among compression rate, distortion, and perceptual quality. By developing a theoretical framework that incorporates common information and conditional rate–distortion–perception functions, and by employing a stochastic cyclic shift operator to jointly handle distortion and perception constraints in both encoding and decoding, the authors derive a first-order asymptotically optimal characterization of the rate–distortion–perception region. This contribution extends the classical point-to-point rate–distortion–perception theory to the multiterminal setting, establishing a rigorous theoretical foundation for applications such as image and video compression.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Machine Learning: Information Theory
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We revisit the Gray-Wyner lossy source coding problem and derive the first-order asymptotic optimal rate-distortion-perception region when additional perception constraints are imposed on reproduced source sequences. The optimal trade-off is shown to be governed by a mutual information term involving common information and two conditional rate-distortion-perception functions. The perception constraint requires that the distribution of each reproduced sequence is close to that of the original source sequence, which is motivated by practical applications in image and video compression. Prior studies usually focus on the compression and reconstruction of a single source sequence. In this paper, we generalize the prior results for point-to-point systems to the representative multi-terminal setting of the Gray-Wyner problem with two correlated source sequences. In particular, we integrate the analyses of the distortion and the perception constraints by including the random circular shift operator in the encoding and decoding process directly.

Problem

• Rate-Distortion-Perception Tradeoff
• Gray-Wyner Problem
• Perception Constraint
• Lossy Source Coding
• Multi-terminal Compression

Innovation

• Rate-Distortion-Perception Tradeoff
• Gray-Wyner Problem
• Perception Constraint
• Common Information
• Multi-terminal Source Coding