Asymptotic average redundancy of Huffman (and other) block codes

IEEE Transactions on Information Theory

Volumn 46, Issue 7, 2000, Pages 2434-2443

  Szpankowski, Wojciech ^a  

^a Purdue University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; BINARY SEQUENCES; BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; FOURIER TRANSFORMS; INTEGRAL EQUATIONS; OPTIMIZATION; POLYNOMIALS; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS; THEOREM PROVING;

ASYMPTOTIC AVERAGE REDUNDANCY; BINOMIAL DISTRIBUTION; GEOMETRIC DISTRIBUTION; GOLOMB CODE; HUFFMAN CODES; SHANNON-FANO CODE; WEYL CRITERION;

BLOCK CODES;

EID: 0034316563     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.887856     Document Type: Article

References (32)

1. J. Abrahams, Code and parse trees for lossless source encoding, Proc. Compression and Complexity of SEQUENCE'97, Positano, 1998, pp. 145-171.
2. R. Capocelli and A. de Santis, Tight upper bounds on the redundancy of Huffman codes," IEEE Trans. Inform. Theory, vol. 35, pp. 1084-1091, Sept. 1989.
3. New bounds on the redundancy of Huffman codes, IEEE Trans. Information Theory, vol. 37, pp. 1095-1104, July 1991.
4. R. Corless, G. Gönnet, D. Hare, D. Jeffrey, and D. Knuth, On the lambert W function," Adv. Computat. Math., vol. 5, pp. 329-359, 1996.
5. T. Cover and J. A. Thomas, Elements of Information Theory. New York: Wiley, 1991.
6. M. Drmota, private communication.
7. M. Drmota and R. Tichy, Sequences, Discrepancies, and Applications. Berlin, Heidelberg, Germany: Springer-Verlag, 1997.
8. R. Gallager, Information Theory and Reliable Communications. New York: Wiley, 1968.
9. Variations on the theme by Huffman, IEEE Trans. Inform. Theory, vol. IT-24, pp. 668-674, Nov. 1978.
10. R. Gallager and D. van Voorhis, Optimal source codes for geometrically distributed integer alphabets, IEEE Trans. Inform. Theory, vol. IT-21, pp. 228-230, Mar. 1975.
11. S. Golomb, Run-length coding, IEEE Trans. Inform. Theory, vol. IT-12, pp. 399-401, July 1966.
12. R. M. Gray, Quantization noise spectra, IEEE Trans. Inform. Theory, vol. 36, pp. 1220-1244, Nov. 1990.
13. D. Huffman, A method for the construction of minimum redundancy codes, Proc. IRE, vol. 40, pp. 1089-1101, 1952.
14. P. Jacquet and W. Szpankowski, Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees, Theor. Comput. Sei, vol. 144, pp. 161-197, 1995.
15. Entropy computations via analytic depoissonization, IEEE Trans. Inform. Theory, vol. 45, pp. 1072-1081, May 1999.
16. L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences. New York: Wiley, 1974.
17. G. Louchard and W. Szpankowski, On the average redundancy rate of the Lempel-Ziv code, IEEE Trans. Inform. Theory, vol. 43, pp. 2-8, Jan. 1997.
18. D. Manstetten, Tight upper bounds on the redundancy of Huffman codes, IEEE Trans. Inform. Theory, vol. 38, pp. 144-151, Jan. 1992.
19. N. Merhav, G. Seroussi, and M. Weinberger, Optimal prefix codes for sources with two-sided geometric distributions, IEEE Trans. Inform. Theory, vol. 46, pp. 121-135, Jan. 2000.
20. F. Olver, Asymptotics and Special Functions. New York: Academic, 1974.
21. J. Rissanen, Complexity of strings in the class of Markov sources, IEEE Trans. Inform. Theory, vol. IT-32, pp. 526-532, July 1986.
22. S. Savari, Variable-to-fixed length codes for predictable sources, Proc. Data Compression Conf., Snowbird, UT, 1998, pp. 481190.
23. S. Savari and R. Gallager, Generalized Tunstall codes for sources with memory, IEEE Trans. Inform. Theory, vol. 43, pp. 658-668, Mar. 1997.
24. Y. Shtarkov, Universal sequential coding of single messages, Probl. Inform. Transm., vol. 23, pp. 175-186, 1987.
25. P. Stubley, On the redundancy of optimum fixed-to-variable length codes, Proc. Data Compression Conf., Snowbird, UT, 1994, pp. 90-97.
26. The Redundancy of Optimum Codes for Multinomially Distributed Sources, 1998. Preprint.
27. W. Szpankowski, On asymptotics of certain recurrences arising in universal coding, Probl. Inform. Transm., vol. 34, no. 2, pp. 55-61, 1998.
28. Average Case Analysis of Algorithms in Sequences. New York: Wiley, 2000.
29. M. Weinberger, N. Merhav, and M. Feder, Optimal sequential probability assignments for individual sequences, IEEE Trans. Inform. Theory, vol. 40, pp. 384-396, Mar. 1994.
30. F. M. Willems, Y. Shtarkov, and T. Tjalkens, The context-tree weighting method: Basic properties, IEEE Trans. Inform. Theory, vol. 41, pp. 653-664, May 1995.
31. J. Ziv, Back from infinity: A constrained resources approach to information theory, IEEE Inform. Theory Soc. Newslett., vol. 48, pp. 30-33, Mar. 1998.
32. A. Zygmund, Trigonometric Series. New York: Cambridge Univ. Press, 1959.