Entropy computations via analytic depoissonization

IEEE Transactions on Information Theory

Volumn 45, Issue 4, 1999, Pages 1072-1081

  Jacquet, Philippe ^a   Szpankowski, Wojciech ^a  

^a INRIA ROCQUENCOURT   (France)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; MATHEMATICAL TRANSFORMATIONS;

ANALYTIC DEPOISSONIZATION; ANALYTIC POISSONIZATION; RENYI ENTROPY; SHANNON ENTROPY;

INFORMATION THEORY;

EID: 0032642947     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.761251     Document Type: Article

References (36)

1. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions. New York: Dover, 1964.
2. D. Aldous, Probability Approximations via the Poisson Clumping Heuristic. New York: Springer-Verlag, 1989.
3. S. Chang and E. Weldon Coding for T-user multiple-access channels," IEEE Trans. Inform. Theory, vol. IT25, pp. 684-691, 1979.
4. L. Comtet, Advanced Combinatorics. Dordrecht, The netherlands: Reidel, 1974.
5. A. D'yachkov and P. Vilenkin Asymptotics of the Shannon and Rényi entropies for sums of independent random variables," in Proc. ISIT'98 (MIT, Cambridge, MA, 1998), p. 376.
6. G. Doetsch, Handbuch der Laplace Transformation, vols. 1-3. Basel, Switzerland: Birkhäuser-Verlag, 1955.
7. M. Drmota and U. Schmid The analysis of the expected successful operation time of slotted ALOHA," IEEE Trans. Inform. Theory, vol. 39, pp. 1567-1577, 1993.
8. G. Fayolle, P. Flajolet, M. Hofri, and P. Jacquet Analysis of stack algorithm for random multiple-access communication," IEEE Trans. Inform. Theory, vol. IT31, pp. 244-254, 1985.
9. P. Flajolet Singularity analysis and asymptotics of Bernoulli sums," Theor. Comput. Sci., vol. 275, pp. 371-387, 1999.
10. P. Flajolet and A. Odlyzko Singularity analysis of generating functions," SIAM J. Discr. Methods, vol. 3, pp. 216-240, 1990.
11. P. Flajolet and R. Sedgewick Analytical combinatorics," in preparation; see also INRIA Tech. Reps. TR-1888 1993, TR-2026 1993, and TR-2376 1994.
12. B. Hughes and A. B. Cooper Near optimal multiuser codes for Binary adder channel," IEEE Trans. Inform. Theory, vol. 42, pp. 387-398, 1996.
13. P. Jacquet Analytical information theory in service of queueing with aggregated up/down arrivals," in Proc. 35th Allerton Conf. (Monticello, IL, 1997), pp. 242-251.
14. P. Jacquet and W. Szpankowski Analysis of digital tries with Markovian dependency," IEEE Trans. Inform. Theory, vol. 37, pp. 1470-1475, 1991.
15. _ Autocorrelation on words and its applications, analysis of suffix trees by string-ruler approach," J. Combin. Theory Ser. A, vol. 66, pp. 237-269, 1994.
16. _ Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees," Theor. Comput. Sci., no. 144, pp. 161-197, 1995.
17. _ Analytical depoissonization and its applications," Theor. Comput. Sci., no. 201, pp. 1-62, 1998.
18. T. Kawabata Exact analysis of the Lempel-Ziv algorithm for i.i.d. sources," IEEE Trans. Inform. Theory, vol. 39, pp. 698-702, 1993.
19. C. Knessl Integral representations and asymptotic expansions for shannon and renyi entropies," Appl. Math. Lett., vol. 11, pp. 69-74, 1998.
20. D. E. Knuth, The Art of Programming, vois. I-III. Reading, MA: Addison Wesley, 1973 and 1981.
21. C. Krattenhaler and P. Slater Asymptotic redundancy for universal quantum coding," preprint.
22. R. Krichevskiy Laplace's law of succession and universal coding," IEEE Trans. Inform. Theory, vol. 44, pp. 296-303, 1998.
23. G. Louchard and W. Szpankowski Average profile and limiting distribution for a phrase size in the Lempel-Ziv parsing algorithm," IEEE Trans. Inform. Theory, vol. 41, pp. 478-488, 1995.
24. _ On the average redundancy rate of the Lempel-Ziv code," IEEE Trans. Inform. Theory, vol. 43, pp. 2-8, 1997.
25. G. Louchard, W. Szpankowski, and J. Tang Average profile for the generalized digital search trees and the generalized Lempel-Ziv algorithm, SIAM J. Comput., 1999.
26. H. Mahmoud, Evolution of Random Search Trees. New York: Wiley, 1992.
27. P. Mathys and P. Flajolet Q-ary collision resolution algorithms in random-access systems with free and blocked channel access," IEEE Trans. Inform. Theory, vol. IT31, pp. 217-243, 1985.
28. A. Odlyzko Asymptotic enumeration," in Handbook of Combinatorics, vol. II, R. Graham, M. Götschel, and L. Lovâsz, Eds. Amsterdam, The Netherlands: Elsevier Science, 1995, pp. 1063-1229.
29. A. Renyi On measures of entropy and information," in Proc. 4th Berkeley Symp. Math. Statist, and Prob., 1961, pp. 547-561.
30. M. Régnier and P. Jacquet New results on the size of tries," IEEE Trans. Inform. Theory, vol. 35, pp. 203-205, 1989.
31. R. Sedgewick and P. Flajolet, Analysis of Algorithms. Reading, MA: Addison Wesley, 1995.
32. W. Szpankowski On a recurrence equation arising in the analysis of conflict resolution algorithms," Stock. Models, vol. 3, pp. 89-114, 1987.
33. _ On asymptotics of certain sums arising in coding theory," IEEE Trans. Inform. Theory, vol. 41, pp. 2087-2090, 1995.
34. _ On asymptotics of certain recurrences arising in universal coding," Probl. Inform. Transm., vol. 34, no. 2, pp. 55-61, 1998.
35. _ Average case analysis of algorithms," in Handbook of Algorithms and Theory of Computation, M. Atallah, Ed. Boca Raton, EL: CRC Press, 1998, eh. 14, pp. 14.1-14.38.
36. H. Wilf, Generatingfunctionology. Boston, MA: Academic, 1990. [37] J. Ziv Back from infinity: A constrained resources approach to information theory," IEEE Inform. Theory Soc. Newstett., vol. 48, pp. 30-33, 1998.