AI summaryⓘ
The authors propose a new framework called Rényi Rate-Distortion-Perception-Privacy (R-RDPP) for encoding information when the source data is indirectly observed through a noisy version. They measure communication cost and privacy leakage using advanced information measures known as Sibson's and Rényi mutual information. Their work includes a detailed study of a Gaussian example showing that usual privacy measures can harm the ability to recover meaningful information. To fix this, they suggest a conditional privacy measure focusing only on leftover privacy risk. They also improve technical bounds by using a method based on Poisson processes, which gives exact formulas for certain entropy measures and tighter performance guarantees.
Rényi mutual informationRate-distortion theoryPrivacy leakageSibson's mutual informationIndirect source codingGaussian sourcePoisson functional representationSemantic distortionEntropyInformation-theoretic privacy
Authors
Jiahui Wei, Marios Kountouris
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.