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Entropy 2015, 17(4), 1936-1945;

On Nonlinear Complexity and Shannon’s Entropy of Finite Length Random Sequences

School of Software, Nanchang University, Nanchang 330031, China
Faculty of Science, Nanchang Institute of Technology, Nanchang 330099, China
Author to whom correspondence should be addressed.
Academic Editor: J.A. Tenreiro Machado
Received: 25 January 2015 / Revised: 18 March 2015 / Accepted: 18 March 2015 / Published: 1 April 2015
(This article belongs to the Section Complexity)
Full-Text   |   PDF [1033 KB, uploaded 1 April 2015]


Pseudorandom binary sequences have important uses in many fields, such as spread spectrum communications, statistical sampling and cryptography. There are two kinds of method in evaluating the properties of sequences, one is based on the probability measure, and the other is based on the deterministic complexity measures. However, the relationship between these two methods still remains an interesting open problem. In this paper, we mainly focus on the widely used nonlinear complexity of random sequences, study on its distribution, expectation and variance of memoryless sources. Furthermore, the relationship between nonlinear complexity and Shannon’s entropy is also established here. The results show that the Shannon’s entropy is strictly monotonically decreased with nonlinear complexity. View Full-Text
Keywords: entropy; nonlinear complexity; random binary sequence entropy; nonlinear complexity; random binary sequence
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.; Liu, B. On Nonlinear Complexity and Shannon’s Entropy of Finite Length Random Sequences. Entropy 2015, 17, 1936-1945.

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