Permutation Entropy for Random Binary Sequences

Entropy

Lingfeng Liu²  Suoxia Miao⁴  Mengfan Cheng¹  Xiaojing Gao³ 

[1] School of Optical and Electronic Information, Huazhong University of Science & Technology, Wuhan 430074, China;;School of Software, Nanchang University, Nanchang 330031, ChinaSchool of Automation, Huazhong University of Science & Technology, Wuhan 430074, China;Faculty of Science, Nanchang Institute of Technology, Nanchang 330099, China;

关键词: permutation entropy;    random binary sequences;    complexity;   

DOI  :  10.3390/e17127872

来源: mdpi

【 摘 要 】

In this paper, we generalize the permutation entropy (PE) measure to binary sequences, which is based on Shannon’s entropy, and theoretically analyze this measure for random binary sequences. We deduce the theoretical value of PE for random binary sequences, which can be used to measure the randomness of binary sequences. We also reveal the relationship between this PE measure with other randomness measures, such as Shannon’s entropy and Lempel–Ziv complexity. The results show that PE is consistent with these two measures. Furthermore, we use PE as one of the randomness measures to evaluate the randomness of chaotic binary sequences.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.