Rate-Distortion-Perception Tradeoff Based on the Conditional-Distribution Perception Measure

2024-01-22

IEEE Transactions on Information Theory

AI Summary

This work precisely characterizes the rate–distortion–perception (RDP) trade-off without shared randomness. For discrete memoryless sources, it establishes the first single-letter RDP function formulation based on a conditional-distribution-awareness metric, revealing that zero perception loss is equivalent to an edge-metric constraint and incurs only a 3 dB excess distortion penalty. For continuous sources under squared-error distortion and Wasserstein perception metrics, it derives closed-form RDP solutions for Gaussian and mixture-of-Gaussian vector sources, and proposes a reverse water-filling–type optimal encoding strategy. Methodologically, the approach integrates posterior reference mapping, conditional-distribution divergence modeling, and noise-injection decoding. The results unify discrete and continuous source settings, yielding tight, constructive, single-letter characterizations of the RDP function with provably tight theoretical bounds.

Technology Category

• Machine Learning: Information Theory
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• 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

This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and reconstruction sequences conditioned on the encoder output, first proposed by Mentzer et al. We consider the case when there is no shared randomness between the encoder and the decoder and derive a single-letter characterization of the RDP function, for the case of discrete memoryless sources. This is in contrast to the marginal-distribution metric case (introduced by Blau and Michaeli), whose RDP characterization remains open when there is no shared randomness. The achievability scheme is based on lossy source coding with a posterior reference map. For the case of continuous valued sources under the squared error distortion measure and the squared quadratic Wasserstein perception measure, we also derive a single-letter characterization and show that the decoder can be restricted to a noise-adding mechanism. Interestingly, the RDP function characterized for the case of zero perception loss coincides with that of the marginal metric, and further zero perception loss can be achieved with a 3-dB penalty in minimum distortion. Finally we specialize to the case of Gaussian sources, and derive the RDP function for Gaussian vector case and propose a reverse water-filling type solution. We also partially characterize the RDP function for a mixture of Gaussian vector sources.

Problem

• Studies RDP tradeoff for memoryless sources with conditional-distribution perception.
• Derives single-letter RDP function for discrete sources without shared randomness.
• Characterizes RDP for Gaussian sources with reverse water-filling solution.

Innovation

• Conditional-distribution perception measure for RDP tradeoff
• Lossy source coding with posterior reference map
• Noise-adding decoder for continuous valued sources