Rényi Rate-Distortion-Perception-Privacy Tradeoff under Indirect Observation

2026-05-10

AI Summary

This work addresses the joint trade-off among communication rate, semantic distortion, perceptual realism, and privacy leakage in scenarios where the encoder has access only to noisy observations. To this end, the authors propose a rate–distortion–perception–privacy (R-RDPP) framework grounded in Rényi information measures. The framework introduces a conditional privacy metric to avoid penalizing legitimate semantic reconstruction and employs Sibson’s α-mutual information to unify the characterization of communication cost and privacy leakage. By leveraging a Gaussian scalar model, geometric mixture distributions, and Poisson functional representations, the authors derive closed-form achievable bounds on integer-order Rényi entropy for α > 1. In the Gaussian setting, they fully characterize the R-RDPP region, yielding performance bounds that are tighter, computationally tractable, and, in certain parameter regimes, superior to those obtained via existing log-moment methods.

Abstract

We introduce a Rényi Rate-Distortion-Perception-Privacy (R-RDPP) framework for indirect source coding. A latent source~$S$ is correlated with a private attribute~$U$, and the encoder observes only a noisy view~$X$ such that $(S,U) - X - Y$ holds at the decoder output~$Y$. The communication cost is measured by Sibson's $α$-mutual information $\Ialp$, the privacy leakage by $\Ibeta$, the semantic distortion between $S$ and $Y$, and the realism constraint at the semantic marginal $P_S$. We characterize the scalar Gaussian RDPP tradeoff, revealing that standard privacy metrics inherently penalize legitimate semantic recovery. To resolve this, we introduce a conditional privacy measure that quantifies only the residual leakage. In addition, we refine the achievability bounds for $α> 1$ via the Poisson functional representation. By deriving the exact geometric-mixture distribution of the Poisson index, we obtain exact closed-form expressions for integer-order Rényi entropies and sharper computable bounds in regimes where the resulting expression improves the logarithmic-moment approach.

Problem

• Rate-Distortion
• Perception
• Privacy
• Indirect Observation
• Rényi Information

Innovation

• Rényi information
• indirect source coding
• conditional privacy
• Poisson functional representation
• rate-distortion-perception-privacy tradeoff