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

• URL: http://arxiv.org/abs/2409.02388v1
• Date: Wed, 4 Sep 2024 02:31:53 GMT
• Title: Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization
• Authors: Li Xie, Liangyan Li, Jun Chen, Lei Yu, Zhongshan Zhang,
• Abstract summary: This paper investigates the best known bounds on the quadratic Gaussian distortion-rate-perception function with limited common randomness. The bounds are nondegenerate in the sense that they cannot be deduced from each other via a refined version of Talagrand's transportation inequality. An improved lower bound is established when the perception measure is given by the squared Wasserstein-2 distance.
• Score: 12.575809787716771
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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