Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization
<|reference_start|>Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization: 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.<|reference_end|>
@article{xie2024gaussian,
    title={Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained
  Scalar Quantization},
    author={Li Xie, Liangyan Li, Jun Chen, Lei Yu, Zhongshan Zhang},
    journal={arXiv preprint arXiv:2409.02388},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.02388},
    primaryClass={cs.IT cs.LG math.IT}
}