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

This paper investigates the tightness of existing bounds on the quadratic Gaussian distortion-rate-perception functions with limited common randomness and the i.i.d. output constraint, under perception measures based on the Kullback–Leibler divergence and the squared Wasserstein-2 distance. For the squared Wasserstein-2 distance-based perception measure, we improve the best-known lower bound by introducing a tunable parameter. Moreover, via the connection between rate-distortion-perception coding and entropy-constrained scalar quantization, it is revealed that all existing bounds, including the improved one, are generally not tight in the weak perception constraint regime. Our findings shed light on the information-theoretic performance limits of rate-distortion-perception coding and offer guidelines for developing practical schemes.