研究高斯信源在感知约束下的编码界限，发现现有理论不紧并提出改进下界。
Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization
- 通过可调参数改进感知约束下的编码下界
- 证明现有界限不可互相推导，且在弱感知时非紧
- 揭示率失真感知编码与熵约束量化的关系
本文研究了在有限公共随机性条件下，基于Kullback-Leibler散度的感知度量和最近由Xie等人建立的基于平方Wasserstein-2距离的感知度量下，二次高斯失真-率-感知函数的最佳已知界限。这些界限被证明是非退化的，即无法通过改进版Talagrand运输不等式相互推导。另一方面，当感知度量为平方Wasserstein-2距离时，建立了更优的下界。此外，通过揭示率失真-感知编码与熵约束标量量化之间的联系，表明在弱感知约束情形下，上述所有界限通常都不是紧的。
原文摘要 · Abstract (English)
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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