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Entropy 2015, 17(12), 8207-8216;

Permutation Entropy for Random Binary Sequences

School of Software, Nanchang University, Nanchang 330031, China
Faculty of Science, Nanchang Institute of Technology, Nanchang 330099, China
School of Optical and Electronic Information, Huazhong University of Science & Technology, Wuhan 430074, China
School of Automation, Huazhong University of Science & Technology, Wuhan 430074, China
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 6 September 2015 / Revised: 24 November 2015 / Accepted: 7 December 2015 / Published: 15 December 2015
(This article belongs to the Section Information Theory, Probability and Statistics)
PDF [2007 KB, uploaded 15 December 2015]


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. View Full-Text
Keywords: permutation entropy; random binary sequences; complexity permutation entropy; random binary sequences; complexity

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Liu, L.; Miao, S.; Cheng, M.; Gao, X. Permutation Entropy for Random Binary Sequences. Entropy 2015, 17, 8207-8216.

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