The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems

Physica D: Nonlinear Phenomena

Volumn 210, Issue 1-2, 2005, Pages 77-95

  Amigó, José M ^a   Kennel, Matthew B ^b   Kocarev, Ljupco ^b  

^a MIGUEL HERNÁNDEZ UNIVERSITY   (Spain)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Entropy; Kolmogorov Sinai entropy; Permutation entropy; Symbolic dynamics

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; INFORMATION ANALYSIS; METRIC SYSTEM; STOCHASTIC CONTROL SYSTEMS;

DETERMINISTIC SYSTEMS; KOLMOGOROV-SINAI ENTROPY; PERMUTATION ENTROPY; SYMBOLIC DYNAMICS;

ENTROPY;

EID: 24644471501     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.07.006     Document Type: Article

References (15)

1. J.M. Amigó, J. Szczepanski, E. Wajnryb, and M.V. Sanchez-Vives Estimating the entropy of spike trains via Lempel-Ziv complexity Neural Comput. 16 2004 717 736
2. C. Bandt, G. Keller, and B. Pompe Entropy of interval maps via permutations Nonlinearity 15 2002 1595 1602
3. C. Bandt, and B. Pompe Permutation entropy: A natural complexity measure for time series Phys. Rev. Lett. 88 2002 174102
4. M. Buhl, and M.B. Kennel Statistically relaxing to generating partitions for observed time-series data Phys. Rev. E 71 2005 046213
5. T.M. Cover, and J.A. Thomas Elements of Information Theory 1991 John Wiley & Sons New York
6. R.M. Gray Entropy and Information Theory 1990 Springer Verlag New York
7. A. Katok, and B. Hasselbaltt Introduction to the Theory of Dynamical Systems 1998 Cambridge University Press Cambridge
8. M.B. Kennel, and A.I. Mees Context-tree modeling of observed symbolic dynamics Phys. Rev. E 66 2002 056209
9. M.B. Kennel, J. Shlens, H.D.I. Abarbanel, and E.J. Chichilnisky Estimating entropy rates with Bayesian confidence intervals Neural Comput. 17 2005 1531 1576
10. I. Kontoyiannis, P.H. Algoet, Y.M. Suhov, and A.J. Wyner Nonparametric entropy estimation for stationary processes and random fields, with applications to English text IEEE Trans. Inform. Theory 44 1998 1319 1327
11. A. Lempel, and J. Ziv On the complexity of an individual sequence IEEE Trans. Inform. Theory IT-22 1976 75 78
12. M. Misiurewicz Permutations and topological entropy for interval maps Nonlinearity 16 2003 971 976
13. S.P. Strong, R. Koberle, R.R. de Ruyter van Steveninck, and W. Bialek Entropy and information in neural spike trains Phys. Rev. Lett. 80 1998 197 200
14. P. Walters An Introduction to Ergodic Theory 2000 Springer Verlag New York
15. J. Ziv, and A. Lempel Compression of individual sequences via variable-rate coding IEEE Trans. Inform. Theory IT-24 1978 530 536