A Constrained BA Algorithm for Rate-Distortion and Distortion-Rate Functions

作     者：Chen, Lingyi Wu, Shitong Ye, Wenhao Wu, Huihui Zhang, Wenyi Wu, Hao Bai, Bo 

作者机构：Department of Mathematical Sciences Tsinghua University Beijing100084 China  University of Electronic Science and Technology of China Huzhou Zhejiang313000 China Theory Lab Center Research Institute 2012 Labs Huawei Technologies Co. Ltd. Hong Kong Department of Electronic Engineering and Information Science University of Science and Technology of China Anhui Hefei230027 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Constrained optimization 

摘      要：The Blahut-Arimoto (BA) algorithm has played a fundamental role in the numerical computation of rate-distortion (RD) functions. This algorithm possesses a desirable monotonic convergence property by alternatively minimizing its Lagrangian with a fixed multiplier. In this paper, we propose a novel modification of the BA algorithm, wherein the multiplier is updated through a one-dimensional root-finding step using a monotonic univariate function, efficiently implemented by Newton s method in each iteration. Consequently, the modified algorithm directly computes the RD function for a given target distortion, without exploring the entire RD curve as in the original BA algorithm. Moreover, this modification presents a versatile framework, applicable to a wide range of problems, including the computation of distortion-rate (DR) functions. Theoretical analysis shows that the outputs of the modified algorithms still converge to the solutions of the RD and DR functions with rate O(1/n), where n is the number of iterations. Additionally, these algorithms provide ϵ-approximation solutions with O _ MNlogN ϵ (1+log|logϵ|) arithmetic operations, where M,N are the sizes of source and reproduced alphabets respectively. Numerical experiments demonstrate that the modified algorithms exhibit significant acceleration compared with the original BA algorithms and showcase commendable performance across classical source distributions such as discretized Gaussian, Laplacian and uniform sources. © 2023, CC BY.