Compression of low entropy strings with Lempel-Ziv algorithms

SIAM Journal on Computing

Volumn 29, Issue 3, 2000, Pages 893-911

  Kosaraju, S Rao ^a   Manzini, Giovanni ^b,c  

^a Johns Hopkins University   (United States)

^b UNIVERSITY OF EASTERN PIEDMONT   (Italy)

^c CNR   (Italy)

Author keywords

Data compression; Empirical entropy; Lempel Ziv parsing

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; DECODING; ENCODING (SYMBOLS); PROBABILITY DISTRIBUTIONS;

LEMPEL-ZIV ALGORITHMS; LOW ENTROPY STRINGS;

DATA COMPRESSION;

EID: 0033294876     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539797331105     Document Type: Article

References (24)

1. T. BELL, I. WITTEN, AND J. CLEARY, Modelling for text compression, ACM Computing Surveys, 21 (1989), pp. 557-592.
2. P. BENDER AND J. WOLF, New asymptotic bounds and improvements on the Lempel-Ziv data compression algorithm, IEEE Trans. Inform. Theory, 37 (1991), pp. 721-729.
3. J. BENTLEY, D. SLEATOR, R. TARJAN, AND V. WEI, A locally adaptive data compression scheme, Comm. ACM, 29 (1986), pp. 320-330.
4. C. BLOOM, LZP: A new data compression algorithm, in Proceedings of the IEEE Data Compression Conference, Snowbird, UT, 1996.
5. T. M. COVER AND J. A. THOMAS, Elements of Information Theory, John Wiley & Sons, New York, 1991.
6. G. HANSEL, D. PERRIN, AND I. SIMON, Compression and entropy, in Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Comput. Sci. 577, Springer, Berlin, 1992, pp. 515-528.
7. P. JACQUET AND W. SZPANKOWSKI, Asymptotic behaviour of the Lempel-Ziv parsing scheme in digital search trees, Theoret. Comput. Sci., 144 (1995), pp. 161-197.
8. T. KAWABATA, Exact analysis of the Lempel-Ziv algorithm for I. I. D. sources, IEEE Trans. Inform. Theory, 39 (1993), pp. 698-708.
9. G. LOUCHARD AND W. SZPANKOWSKI, On the average redundancy rate of the Lempel-Ziv code, IEEE Trans. Inform. Theory, 43 (1997), pp. 2-8.
10. H. MORITA AND K. KOBAYASHI, On asymptotic optimality of a sliding window variation of Lempel-Ziv codes, IEEE Trans. Inform. Theory, 39 (1993), pp. 1840-1846.
11. E. PLOTNIK, M. WEINBERGER, AND J. ZIV, Upper bounds on the probability of sequences emitted by finite-state sources and on the redundancy of the Lempel-Ziv algorithm, IEEE Trans. Inform. Theory, 38 (1992), pp. 66-72.
12. M. RODEH, V. PRATT, AND S. EVEN, Linear algorithm for data compression via string matching, J. ACM, 28 (1981), pp. 16-24.
13. D. SALOMON, Data Compression: The Complete Reference, Springer-Verlag, New York, 1997.
14. S. SAVARI, Redundancy of the Lempel-Ziv incremental parsing rule, IEEE Trans. Inform. Theory, 43 (1997), pp. 9-21.
15. S. SAVARI, Redundancy of the Lempel-Ziv string matching code, IEEE Trans. Inform. Theory, 44 (1998), pp. 787-791.
16. D. SHEINWALD, On the Ziv-Lempel proof and related topics. Proc. IEEE, 82 (1994), pp. 866-871.
17. W. SZPANKOWSKI, Asymptotic properties of data compression and suffix trees, IEEE Trans. Inform. Theory, 39 (1993), pp. 1647-1659.
18. A. WYNER AND A. WYNER, Improved redundancy of a version of the Lempel-Ziv algorithm, IEEE Trans. Inform. Theory, 41 (1995), pp. 723-731.
19. A. WYNER AND J. ZIV, Fixed data base version of the Lempel-Ziv data compression algorithm, IEEE Trans. Inform. Theory, 37 (1991), pp. 878-880.
20. A. WYNER AND J. ZIV, The sliding-window Lempel-Ziv algorithm is asymptotically optimal, Proc. IEEE, 82 (1994), pp. 872-877.
21. A. J. WYNER, The redundancy and distribution of the phrase lengths in the fixed-database Lempel-Ziv algorithm, IEEE Trans. Inform. Theory, 43 (1997), pp. 1452-1464.
22. E. YANG AND J. KIEFFER, On the performance of data compression algorithms based on string matching, IEEE Trans. Inform. Theory, 44 (1998), pp. 47-65.
23. J. ZIV AND A. LEMPEL, A universal algorithm for sequential data compression, IEEE Trans. Inform. Theory, 23 (1977), pp. 337-343.
24. J. ZIV AND A. LEMPEL, Compression of individual sequences via variable-rate coding, IEEE Trans. Inform. Theory, 24 (1978), pp. 530-536.