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.

翻译：我们针对间接信源编码提出了一种Rényi率-失真-感知-隐私（R-RDPP）框架。潜在信源$S$与私有属性$U$相关，编码器仅观测到带噪视点$X$，使得在解码器输出$Y$处满足$(S,U) - X - Y$的关系。通信成本由Sibson $α$-互信息$\Ialp$度量，隐私泄露用$\Ibeta$衡量，同时考虑$S$与$Y$之间的语义失真，以及语义边缘分布$P_S$上的真实性约束。我们刻画了标量高斯情况下的RDPP权衡关系，揭示出标准隐私度量固有地惩罚了合理的语义恢复。为解决这一问题，我们引入一种条件隐私度量，仅量化残余泄露量。此外，我们通过泊松函数表示改进了$α>1$情况下的可达界。通过推导泊松索引的精确几何混合分布，我们获得了整数阶Rényi熵的精确闭式表达式，并在所得表达式优于对数矩方法的区域中得到了更紧的可计算界。