A Revisit to Rate-distortion Theory via Optimal Weak Transport
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913663811584000 |
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| author | Zou, Jiayang Fan, Luyao Gao, Jiayang Wang, Jia |
| author_facet | Zou, Jiayang Fan, Luyao Gao, Jiayang Wang, Jia |
| contents | This paper revisits the rate-distortion theory from the perspective of optimal weak transport, as recently introduced by Gozlan et al. While the conditions for optimality and the existence of solutions are well-understood in the case of discrete alphabets, the extension to abstract alphabets requires more intricate analysis. Within the framework of weak transport problems, we derive a parametric representation of the rate-distortion function, thereby connecting the rate-distortion function with the Schrödinger bridge problem, and establish necessary conditions for its optimality. As a byproduct of our analysis, we reproduce K. Rose's conclusions regarding the achievability of Shannon lower bound concisely, without reliance on variational calculus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Revisit to Rate-distortion Theory via Optimal Weak Transport Zou, Jiayang Fan, Luyao Gao, Jiayang Wang, Jia Information Theory This paper revisits the rate-distortion theory from the perspective of optimal weak transport, as recently introduced by Gozlan et al. While the conditions for optimality and the existence of solutions are well-understood in the case of discrete alphabets, the extension to abstract alphabets requires more intricate analysis. Within the framework of weak transport problems, we derive a parametric representation of the rate-distortion function, thereby connecting the rate-distortion function with the Schrödinger bridge problem, and establish necessary conditions for its optimality. As a byproduct of our analysis, we reproduce K. Rose's conclusions regarding the achievability of Shannon lower bound concisely, without reliance on variational calculus. |
| title | A Revisit to Rate-distortion Theory via Optimal Weak Transport |
| topic | Information Theory |
| url | https://arxiv.org/abs/2501.09362 |