Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914935853809664 |
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| author | Xie, Li Li, Liangyan Chen, Jun Yu, Lei Zhang, Zhongshan |
| author_facet | Xie, Li Li, Liangyan Chen, Jun Yu, Lei Zhang, Zhongshan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization Xie, Li Li, Liangyan Chen, Jun Yu, Lei Zhang, Zhongshan Information Theory Machine Learning 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. |
| title | Gaussian Rate-Distortion-Perception Coding and Entropy-Constrained Scalar Quantization |
| topic | Information Theory Machine Learning |
| url | https://arxiv.org/abs/2409.02388 |