Analyzing {\alpha}-divergence in Gaussian Rate-Distortion-Perception Theory

The problem of estimating the information rate distortion perception function (RDPF), which is a relevant information-theoretic quantity in goal-oriented lossy compression and semantic information reconstruction, is investigated here. Specifically, we study the RDPF tradeoff for Gaussian sources subject to a mean-squared error (MSE) distortion and a perception measure that belongs to the family of {\alpha} divergences. Assuming a jointly Gaussian RDPF, which forms a convex optimization problem, we characterize an upper bound for which we find a parametric solution. We show that evaluating the optimal parameters of this parametric solution is equivalent to finding the roots of a reduced exponential polynomial of degree {\alpha}. Additionally, we determine which disjoint sets contain each root, which enables us to evaluate them numerically using the well-known bisection method. Finally, we validate our analytical findings with numerical results and establish connections with existing results.