A suboptimal lossy date compression based on approximate pattern matching

IEEE Transactions on Information Theory

Volumn 43, Issue 5, 1997, Pages 1439-1451

  Łuczak, Tomasz ^b,c   Szpankowski, Wojciech ^a,d  

^a IEEE

^b INSTITUTE OF MATHEMATICS   (Poland)

^c ADAM MICKIEWICZ UNIVERSITY   (Poland)

^d Purdue University   (United States)

Author keywords

Approximate pattern matching; Generalized Lempel Ziv scheme; Generalized R nyi entropy; Lossy data compression; Mixing probabilistic model; Rate distortion

Indexed keywords

ALGORITHMS; ASYMPTOTIC STABILITY; DATA COMPRESSION; DECODING; ERRORS; MATHEMATICAL MODELS; PROBABILITY; SIGNAL DISTORTION;

APPROXIMATE PATTERN MATCHING; GENERALIZED LEMPEL-ZIV SCHEME; GENERALIZED RENYI ENTROPY; MIXING PROBABILISTIC MODEL; RATE DISTORTION; SUBOPTIMAL LOSSY DATA COMPRESSION;

SIGNAL ENCODING;

EID: 0031236412     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.623143     Document Type: Article

References (40)

1. N. Alon and J. Spencer, The Probabilistic Method. New York: Wiley, 1992.
2. R. Arratia and M. Waterman, "The Erdös-Rényi strong law for pattern matching with given proportion of mismatches," Ann. Probab., vol. 17, pp. 1152-1169, 1989.
3. R. Arratia, L. Gordon, and M. Waterman, "The Erdös-Rényi law in distribution for coin tossing and sequence matching," Ann. Statist., vol. 18, pp. 539-570, 1990.
4. M. Atallah, Y. Génin, and W. Szpankowski, "Pattern matching image compression: Algorithmic and empirical results" in Proc. Int. Conf. on Image Processing (Lausanne, Switzerland, 1996), vol. II, pp. 349-352.
5. M. Atallah, P. Jacquet, and W. Szpankowski, "Pattern matching with mismatches: A probabilistic analysis and a randomized algorithm," in Proc. Combinatorial Pattern Matching. (Lecture Notes in Computer Science, vol. 644). Berlin, Germany: Springer-Verlag, 1992, pp. 27-40.
6. T. Berger, Rate Distortion Theory: A Mathematical Basis for Data Compression. Englewood Cliffs, NJ: Prentice-Hall, 1971.
7. P. Chou, M. Effros, and R. Gray, "A vector quantization approach to universal noiseless coding and quantization," IEEE Trans. Inform. Theory, vol. 42, pp. 1109-1138, 1996.
8. C. Constantinescu and J. Storer, "Improved techniques for single-pass adaptive vector quantization," Proc. IEEE, vol. 82, pp. 933-939, 1994.
9. M. Effros and P. Chou, "Weighted universal bit allocation," in Proc. Int. Conf. on Acoustics, Speech, and Signal Processing (Detroit, MI, 1995), vol. 4, pp. 2343-2346.
10. n," Israel J. Math., vol. 86, pp. 321-345, 1980.
11. W. Finamore, M. Carvalho, and J. Kieffer, "Lossy compression with the Lempel-Ziv algorithm," in 11th Brasilian Telecommunication Conf., 1993, pp. 141-146.
12. A. Frieze and W. Szpankowski, "Greedy algorithms for the shortest common superstring that are asymptotically optimal," Algorithmica, to be published;
13. preliminary version in Proc. European Symp. on Algorithms (Lecture Notes in Computer Science, vol. 1136). New York: Springer, 1996, pp. 194-207.
14. G. Hardy, J. E. Littlewood, and G. Pólya, Inequalities. Cambridge, U.K.: Cambridge Univ. Press, 1989.
15. P. Jacquet and W. Szpankowski, "Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees," Theor. Comput. Sci., vol. 144, pp. 161-197, 1995.
16. J. C. Kieffer, "Strong converses in source coding relative to a fidelity criterion," IEEE Trans. Inform. Theory, vol. 37, pp. 257-262, 1991.
17. J. F. C. Kingman, "Subadditive processes," in Ecole d'Eté de Probabilités de Saint-Flour V-1975 (Lecture Notes in Mathematics, vol. 539). Berlin, Germany: Springer-Verlag, 1976, .
18. H. Koga and S. Arimoto, "Asymptotic properties of algorithms of data compression with fidelity criterion based on string matching," in Proc. 1994 IEEE Int. Symp. on Information Theory, 1994, pp. 24-25.
19. T. Linder, G. Lugosi, and K. Zeger, "Rates of convergence in the source coding theorem, in empirical quantizer design, and in universal lossy source coding," IEEE Trans. Inform. Theory, vol. 40, pp. 1728-1740, 1994.
20. _, "Fixed-rate universal lossy source coding and rates of convergence for memoryless sources," IEEE Trans. Inform. Theory, vol. 41, pp. 665-676, 1995.
21. 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.
22. G. Louchard, W. Szpankowski, and J. Tang, "Average profile of generalized digital search trees and the generalized Lempel-Ziv algorithm," SIAM J. Comput., to be published.
23. T. Łuczak and W. Szpankowski, "A lossy data compression based on string matching: Preliminary analysis and suboptimal algorithms," in Proc. Combinatorial Pattern Matching (Lecture Notes in Computer Science, vol. 807). New York: Springer-Verlag, 1994, pp. 102-112.
24. K. Marton and P. Shields, "The positive-divergence and blowing-up properties," Israel J. Math., vol. 80, pp. 331-348, 1994.
25. D. Ornstein and P. Shields, "Universal almost sure data compression," Ann. Probab., vol. 18, pp. 441-452, 1990.
26. D. Ornstein and B. Weiss, "Entropy and data compression schemes," IEEE Trans. Inform. Theory, vol. 39, pp. 78-83, 1993.
27. E. Posner and E. Rodemich, "Epsilon entropy and data compression," Ann. Math. Statist., vol. 42, pp. 2079-2125, 1971.
28. I. Sadeh, "On approximate string matching," in Proc. of Data Compression Conf., 1993, pp. 148-157.
29. Y. Steinberg and M. Gutman, "An algorithm for source coding subject to a fidelity criterion, based on string matching," IEEE Trans. Inform. Theory, vol. 39, pp. 877-886, 1993.
30. P. Shields, "Waiting times: Positive and negative results on the Wyner-Ziv problem," J. Theor. Probab., vol. 6, pp. 499-519, 1993.
31. W. Szpankowski, "Asymptotic properties of data compression and suffix trees," IEEE Trans. Inform. Theory, vol. 39, pp. 1647-1659, 1993.
32. _, "A generalized suffix tree and its (un)expected asymptotic behaviors," SIAM J. Comput., vol. 22, pp. 1176-1198, 1993.
33. A. Wyner and J. Ziv, "Some asymptotic properties of the entropy of a stationary ergodic data source with applications to data compression," IEEE Trans. Inform. Theory, vol. 35, pp. 1250-1258, 1989.
34. E. H. Yang and J. Kieffer, "Simple universal lossy data compression schemes derived from Lempel-Ziv algorithm," IEEE Trans. Inform. Theory, vol. 42, pp. 239-245, 1996.
35. _, "On the performance of data compression algorithms based upon string matching," 1995, preprint.
36. E. H. Yang and Z. Zhang, "The shortest common superstring problem: Average case analysis for both exact matching and approximate matching," 1996, preprint.
37. Z. Zhang and V. Wei, "An on-line universal lossy data compression algorithm via continuous codebook refinement - Part I: Basic results," IEEE Trans. Inform. Theory, vol. 42, pp. 803-821, 1996.
38. J. Ziv, "Coding of source with unknown statistics - Part II: Distortion relative to a fidelity criterion," IEEE Trans. Inform. Theory, vol. IT-18, pp. 389-394, 1972.
39. J. Ziv and A. Lempel, "A universal algorithm for sequential data compression," IEEE Trans. Inform. Theory, vol. IT-23, vol. 337-343, May 1977.
40. _, "Compression of individual sequences via variable-rate coding," IEEE Trans. Inform. Theory, vol. IT-24, pp. 530-536, 1978.