论文标题
通信最佳运输方法计算速率失真函数的计算
A Communication Optimal Transport Approach to the Computation of Rate Distortion Functions
论文作者
论文摘要
在本文中，我们提出了一个名为Communication Optival Transport（COMP）的新框架，用于计算速率失真（RD）函数。这项工作是通过观察到过渡定律和通信理论中的相对熵被视为运输计划和最佳运输（OT）模型中的正则目标函数来激发的。但是，与经典的OT问题不同，RD功能仅具有一侧边缘分布。因此，为了维护OT结构，我们引入了松弛变量以实现其他边缘分布，然后为RD函数提出了一个通用框架（compot）。通过交替的优化技术和众所周知的sndhorn算法来解决COMMOT模型。特别是，可以将预期的失真阈值转换为仅使用几个步骤的一维单调函数的独特根。数值实验表明，我们提出的用于用给定的失真阈值求解RD函数的框架（COMP）是有效而准确的。
In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in communication theory can be viewed as the transport plan and the regularized objective function in the optimal transport (OT) model. However, unlike in classical OT problems, the RD function only possesses one-side marginal distribution. Hence, to maintain the OT structure, we introduce slackness variables to fulfill the other-side marginal distribution and then propose a general framework (CommOT) for the RD function. The CommOT model is solved via the alternating optimization technique and the well-known Sinkhorn algorithm. In particular, the expected distortion threshold can be converted into finding the unique root of a one-dimensional monotonic function with only a few steps. Numerical experiments show that our proposed framework (CommOT) for solving the RD function with given distortion threshold is efficient and accurate.
