R\'enyi Rate-Distortion-Perception-Privacy Tradeoff under Indirect Observation

TL;DR

This paper develops a Re9nyi-based framework for indirect source coding that balances privacy, distortion, and realism, with new measures and bounds for Gaussian models.

Contribution

It introduces a novel Re9nyi Rate-Distortion-Perception-Privacy framework with residual privacy measures and refined bounds for Gaussian sources.

Findings

Characterized the Gaussian RDPP tradeoff revealing privacy penalties.

Proposed a conditional privacy measure to isolate residual leakage.

Derived exact closed-form expressions for Re9nyi entropies in Gaussian models.

Abstract

We introduce a R\'enyi 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 $\alpha$-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 $\alpha > 1$ 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 R\'enyi entropies and sharper computable bounds in regimes where the resulting expression improves the logarithmic-moment approach.