On analytic properties of entropy rate

IEEE Transactions on Information Theory

Volumn 55, Issue 5, 2009, Pages 2119-2127

  Schönhuth, Alexander ^a  

^a SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Analytic properties; Discrete random source; Entropy rate; Evolution dimension; Hidden Markov source; Quantum random walk

Indexed keywords

ANALYTIC PROPERTIES; DISCRETE RANDOM SOURCE; ENTROPY RATE; EVOLUTION DIMENSION; HIDDEN MARKOV SOURCE; QUANTUM RANDOM WALK;

ENTROPY; PERMITTIVITY; TOPOLOGY;

SIGNAL THEORY;

EID: 65749106522     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2016015     Document Type: Article

References (31)

1. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, "Quantum walks on graphs," in Proc. 33rd ACM STOC, New York, NY, 2001, pp. 50-59.
2. P. Billingsley, Ergodic Theory and Information. New York: Wiley, 1965.
3. L. Breiman, "The individual ergodic theorem of information theory," Ann. Math. Statist., vol. 28, pp. 809-811, 1957.
4. L. Breiman, "A correction to 'The individual ergodic theorem of information theory'," Ann. Math. Statist., vol. 31, pp. 809-810, 1960.
5. U. Faigle and A. Schönhuth, "Quantum predictor models," Electron. Notes Discr. Math., vol. 25, pp. 149-155, 2006.
6. U. Faigle and A. Schoenhuth, "Asymptotic mean stationarity of sources with finite evolution dimension," IEEE Trans. Inf. Theory, vol. 53, no. 7, pp. 2342-2348, 2007.
7. H. Federer, Geometric Measure Theory. New York: Springer, 1969.
8. R. Gray and L. Davisson, "The ergodic decomposition of stationary discrete random processes," IEEE Trans. Inf. Theory, vol. 20, pp. 625-636, 1974.
9. R. M. Gray and J. C. Kieffer, "Asymptotically mean stationary measures," Ann. Probabil., vol. 8, pp. 962-973, 1980.
10. R. M. Gray, Entropy and Information Theory. New York: Springer-Verlag, 1990.
11. P. R. Halmos, Measure Theory. New York: Van Nostrand, 1964.
12. T. S. Han and K. Kobayashi, Mathematics of Information and Coding. New York: Amer. Math. Soc., 2002.
13. A. Heller, "On stochastic processes derived from Markov chains," Ann. Math. Statist., vol. 36, no. 4, pp. 1286-1291, 1965.
14. H. Ito, S.-I. Amari, and K. Kobayashi, "Identifiability of hidden Markov information sources and their minimum degrees of freedom," IEEE Trans. Inf. Theory, vol. 38, no. 2, pp. 324-333, 1992.
15. S. D. Jacka and G. O. Roberts, "On strong forms of weak convergence," Stochastic Processes Appl., vol. 67, pp. 41-53, 1997.
16. K. Jacobs, "Die Übertragung diskreter Informationen durch periodische und fastperiodische Kanäle," Mathematische Annalen vol. 137, pp. 125-135, 1959.
17. K. Jacobs, "Über die Struktur der mittleren Entropie," Mathematisches Zentralblatt, vol. 78, pp. 33-43, 1962.
18. P. Jacquet, G. Seroussi, and W. Szpankowski, "On the entropy of a hidden Markov process," in Proc. Data Compression Conf., Snowbird, UT, Mar. 2004, pp. 362-371.
19. J. C. Kieffer and M. Rahe, "Markov channels are asymptotically mean stationary," SIAM J. Math. Anal., vol. 12, no. 3, pp. 293-305, 1981.
20. G. Han and B. Marcus, "Analyticity of entropy rate of hidden Markov chains," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5251-5266, 2006.
21. G. Han and B. Marcus, "Derivatives of entropy rate in special families of hidden Markov chains," IEEE Trans. Inf. Theory, vol. 53, no. 7, pp. 2642-2652, 2007.
22. G. Han and B. Marcus, "Asymptotics of entropy rate of hidden Markov chains at weak black holes," in Proc. IEEE Int. Symp. Inf. Theory 2008, pp. 2629-2633.
23. B. McMillan, "The basic theorems of information theory," Ann. Math. Statist., vol. 24, pp. 196-219, 1953.
24. Y. Ephraim and N. Merhav, "Hidden Markov processes," IEEE Trans. Inf. Theory, vol. 48, no. 6, pp. 1518-1569.
25. E. Ordentlich and T. Weissman, "On the optimality of symbol by symbol filtering and denoising," IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 19-40, 2006.
26. A. Schönhuth, The Ergodic Decomposition of Asymptotically Mean Stationary Random Sources Online. Available: http://arxiv.org/abs/ 0804.2487, submitted for publication
27. A. Schönhuth, "On Analytic Properties of Entropy Rate," Tech. Rep. Univ. Cologne, ZAIK, Cologne, Germany, 2006.
28. A. Schönhuth, A Simple and Efficient Solution of the Identifiability Problem for Hidden Markov Sources and Quantum Random Walks ISITA, 2008 [Online]. Available: http://arxiv.org/abs/0808.2833, to be published
29. C. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., 1948.
30. O. Zuk, E. Domany, I. Kanter, and M. Aizenman, "From finite system entropy to entropy rate for a hidden Markov process," IEEE Signal Process. Lett., vol. 13, pp. 517-520, 2006.
31. O. Zuk, I. Kanter, and E. Domany, "The entropy of a binary hidden Markov process," J. Statist. Phys., vol. 121, no. 3-4, pp. 343-360, 2005.