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arXiv · 2501.09362

A Revisit to Rate-distortion Theory via Optimal Weak Transport

Jiayang Zou·Luyao Fan·Jiayang Gao·Jia Wang
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Abstract

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 Schr\"odinger 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.

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Jiayang Zou, Luyao Fan, Jiayang Gao, Jia Wang. 2025-01-16. A Revisit to Rate-distortion Theory via Optimal Weak Transport. https://arxiv.org/abs/2501.09362

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