一种确定混沌伪随机序列复杂度的模糊关系熵测度

陈小军; 李赞; 白宝明; 蔡觉平

doi:10.7498/aps.60.064215

摘要

将模糊关系的概念引入混沌伪随机序列复杂度的测度方法之中,提出了一种新的混沌伪随机序列复杂度测度方法——模糊关系熵(fuzzy relationship entropy,简记为F-REn)测度方法,并推导了F-REn的两个基本性质.仿真结果表明,该测度方法能够有效测度混沌伪随机序列的复杂度,与近似熵(ApEn)测度方法和符号熵测度方法相比,F-REn测度具有更加好的对序列符号空间的适用性、更加小的对测量维度的敏感性和更加强的对分辨率参数的鲁棒性.

关键词:

Abstract

A new complexity metric to evaluate the unpredictability of the chaotic pseudorandom sequences based on the fuzzy relationship entropy (F-REn) is proposed in the view of maximal randomness of the sequences with arbitrary length. On this condition,two basic properties of F-REn are proved. Simulations and analysis results show that, the proposed F-REn works effectively to discern the changing complexities of the chaotic pseudorandom sequences, and compared with complexity metric based on the approximate entropy(ApEn) and symbolic dynamics approach , F-REn works have obvious advantages in the applicability of symbolic space, the sensitivity of vector dimension and the robustness of resolution parameter.

Keywords:

作者及机构信息

(1)西安电子科技大学微电子学院,西安 710071; (2)西安电子科技大学综合业务网理论及关键技术国家重点实验室,西安 710071

基金项目: 国家科技重大专项(批准号:2010ZX03006-002-04)、国家高技术研究发展计划(批准号:2009AA01Z237)、国家自然科学基金(批准号: 61072070)、教育部新世纪优秀人才支持计划(批准号:NCET-07-0653)、高等学校学科创新引智计划(批准号:B08038)、教育部长江学者和创新团队发展计划(批准号:IRT0852)和陕西省自然科学基础研究计划项目(批准号:SJ08F09)资助的课题.

Authors and contacts

(1)Schoole of Microelectronics,Xidian University, Xi’an 710071,China; (2)State Key Laboratory of Integrated Service Networks (ISN),Xidian University,Xi’an 710071,China

参考文献

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[18]	Xie Y, Xu J X, Yang H J, Hu S J 2002 Acta Phys. Sin. 51 205 (in Chinese) [谢勇、徐健学、杨红军、胡三觉2002 51 205]
[19]	Wang G Q, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光、张增平 2008 57 1976]
[20]	Cao B, Lü X Q, Zeng M, Wang Z M,Hang S S 2006 Acta Phys. Sin. 55 1696 (in Chinese)[曹彪、吕小青、曾敏、王振民、黄石生 2006 55 1696]
[21]	Xiao F H,Yan G R, HanY H 2004 Acta Phys. Sin. 53 1871 (in Chinese) [肖方红、阎桂荣、韩宇航2004 53 2877]
[22]	Azad R K, Rao J S, Ramaswamy R 2002 Chaos, Soliton. Fract. 14 633
[23]	Liu X F, Yu W L 2008 Acta Phys. Sin. 57 2587 (in Chinese) [刘小峰、俞文莉2008 57 2587]
[24]	Hu B Q 2004 Fundemental of Fuzzy Theory (Wuhan:Wuhan University Press) Chapt1—3(in Chinese)[胡宝清 2004 模糊理论基础(武汉: 武汉大学出版社)第1—3章]
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[26]	Chen W, Wang Z Z, Xie H B, Yu W X 2007 IEEE Trans. Neural Syst. Rehabil. Eng. 15 266
[27]	Chen W T, Zhuang J, Yu W X, Wang Z Z 2009 Med. Eng. Phys. 31 61
[28]	Ornstein D, Weiss B 1990 Ann. Probab. 18 905

施引文献

[1]	Heidari-Bateni G, McGillem C D 1994 IEEE Trans. Commun. 42 1524
[2]	Heidari-Bateni G, McGillem C D 1992 Wireless Communications 1992 Conference Proceedings p437
[3]	Zan Li, Jueping Cai, Xiaojun Chen, Xiaofeng Lu 2009 Wireless Communications and Networking Conference, 2009 IEEE, (4) 1—5
[4]	LiZ, Cai J P, Lu X F, Si J B 2009 Communications, 2009. ICC '09. IEEE International Conference on (6) p1—5
[5]	Li Z, Cai J P, Chang Y L 2009 IEEE Trans.Commun. 57 812
[6]	Kolmogorov A N 1965 Problems of Information Transmission 1 4
[7]	Lempel A, Ziv J 1976 IEEE Trans. Inform. Theory 22 75
[8]	Ruepple R A 1984 Ph.D.Dissertation (Zurich: Swiss Federal Institute of Technology)
[9]	Xiao G Z, Wei S M, Lam K Y, Imamura K 2000 IEEE Trans. Inform. Theory 46 2203
[10]	Kolokotronis N, Kalouptsidis N 2003 IEEE Trans. Inform. Theory 49 3047
[11]	Griffin F, Shparlinski I E 2000 IEEE Trans. Inform. Theory 46 2159
[12]	Gutierrez J, Shparlinski I E, Winterhof A 2003 IEEE Trans. Inform. Theory 49 60
[13]	Kurosawa K, Sato F, Sakata T, Kishimoto W 2000 IEEE Trans. Inform. Theory 46 694
[14]	Lauder A G B, Paterson K G 2003 IEEE Trans. Inform. Theory 49 273
[15]	Cai J P, Li Z, Song W T 2003 Acta Phys. Sin. 52 1871 (in Chinese) [蔡觉平、李赞、宋文涛 2003 52 1871]
[16]	Pincus S M 1995 Chaos 5 110
[17]	Zhuang J J, Ning X B, Zou M, Sun B, Yang X 2008 Acta Phys. Sin. 57 2805 (in Chinese) [庄建军、宁新宝、邹鸣、孙飙、杨希2008 57 2805]
[18]	Xie Y, Xu J X, Yang H J, Hu S J 2002 Acta Phys. Sin. 51 205 (in Chinese) [谢勇、徐健学、杨红军、胡三觉2002 51 205]
[19]	Wang G Q, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光、张增平 2008 57 1976]
[20]	Cao B, Lü X Q, Zeng M, Wang Z M,Hang S S 2006 Acta Phys. Sin. 55 1696 (in Chinese)[曹彪、吕小青、曾敏、王振民、黄石生 2006 55 1696]
[21]	Xiao F H,Yan G R, HanY H 2004 Acta Phys. Sin. 53 1871 (in Chinese) [肖方红、阎桂荣、韩宇航2004 53 2877]
[22]	Azad R K, Rao J S, Ramaswamy R 2002 Chaos, Soliton. Fract. 14 633
[23]	Liu X F, Yu W L 2008 Acta Phys. Sin. 57 2587 (in Chinese) [刘小峰、俞文莉2008 57 2587]
[24]	Hu B Q 2004 Fundemental of Fuzzy Theory (Wuhan:Wuhan University Press) Chapt1—3(in Chinese)[胡宝清 2004 模糊理论基础(武汉: 武汉大学出版社)第1—3章]
[25]	ZadehLA 1965 Information and Control 8 338
[26]	Chen W, Wang Z Z, Xie H B, Yu W X 2007 IEEE Trans. Neural Syst. Rehabil. Eng. 15 266
[27]	Chen W T, Zhuang J, Yu W X, Wang Z Z 2009 Med. Eng. Phys. 31 61
[28]	Ornstein D, Weiss B 1990 Ann. Probab. 18 905

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