Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization

TL;DR

This paper explores bounds on the quadratic Gaussian rate-distortion-perception function with limited randomness, revealing their nondegeneracy, improvements under Wasserstein measures, and limitations in weak perception regimes.

Contribution

It establishes nondegenerate bounds for perception measures, improves lower bounds for Wasserstein-based perception, and links rate-distortion-perception coding with entropy-constrained scalar quantization.

Findings

Bounds are nondegenerate and cannot be derived from each other.

An improved lower bound is provided for Wasserstein-2 perception.

Bounds are generally not tight in the weak perception constraint regime.

Abstract

This paper investigates the best known bounds on the quadratic Gaussian distortion-rate-perception function with limited common randomness for the Kullback-Leibler divergence-based perception measure, as well as their counterparts for the squared Wasserstein-2 distance-based perception measure, recently established by Xie et al. These bounds are shown to be nondegenerate in the sense that they cannot be deduced from each other via a refined version of Talagrand's transportation inequality. On the other hand, an improved lower bound is established when the perception measure is given by the squared Wasserstein-2 distance. In addition, it is revealed by exploiting the connection between rate-distortion-perception coding and entropy-constrained scalar quantization that all the aforementioned bounds are generally not tight in the weak perception constraint regime.