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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.
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Keywords:
- chaotic pseudorandom sequences /
- fuzzy theory /
- complexity.
[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 物理学报 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 物理学报 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 物理学报 51 205]
[19] Wang G Q, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光、张增平 2008 物理学报 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 物理学报 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 物理学报 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 物理学报 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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[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 物理学报 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 物理学报 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 物理学报 51 205]
[19] Wang G Q, Zhang Z P 2008 Acta Phys. Sin. 57 1976 (in Chinese) [王启光、张增平 2008 物理学报 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 物理学报 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 物理学报 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 物理学报 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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