Complexities of information sources

Yamin Sayyari; Mohammad Reza Molaei; Adel Mehrpooya

doi:10.1080/02664763.2022.2101631

Complexities of information sources

J Appl Stat. 2022 Jul 21;50(15):3125-3141. doi: 10.1080/02664763.2022.2101631. eCollection 2023.

Authors

Yamin Sayyari¹, Mohammad Reza Molaei², Adel Mehrpooya³

Affiliations

¹ Sirjan University of Technology, Sirjan, Iran.
² Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran.
³ School of Mathematical Sciences, Faculty of Science, Queensland University of Technology, Brisbane, Australia.

Abstract

Calculating the entropy for complex systems is a significant problem in science and engineering problems. However, this calculation is usually computationally expensive when the entropy is computed directly. This paper introduces three classes of information sources that for all members of each class, the entropy value is the same. These classes are characterized according to special dynamics created by three kinds of self-mappings on Ω, and A, where Ω is a probability space and A is a finite set. An approximation of rank variables of the product of information sources is made, and it is proved that the topological entropy of the product of two information sources is equal to the summation of their topological entropies.

Keywords: 37B40; 37M25; 54C70; 94A17; Topological entropy; information source; metric entropy; permutation metric entropy; permutation topological entropy; quantum information system.