An on-line universal lossy data compression algorithm via continuous codebook refinement-part II: Optimality for phi-mixing source models

IEEE Transactions on Information Theory

Volumn 42, Issue 3, 1996, Pages 822-836

  Zhang, Zhen ^a   Yang, Rn Hui ^b  

^a University of Southern California ^*  (United States)

^b NANKAI UNIVERSITY   (China)

Author keywords

Distortion rate (rate distortion) function; Gold washing algorithm; O mixing; Stationary and ergodic sources; Universal lossy data compression

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DATA COMPRESSION; ENCODING (SYMBOLS); MARKOV PROCESSES; MATHEMATICAL MODELS; OPTIMIZATION; SET THEORY; VECTOR QUANTIZATION;

DISTORTION RATE FUNCTION; GOLD WASHING ALGORITHM; OPTIMAL CODEBOOK; UNIVERSAL LOSSY DATA COMPRESSION;

ALGORITHMS;

EID: 0030150339     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.490547     Document Type: Article

References (19)

1. R. Ahlswcdc. P. Gâcs, and J. Körner, "Bounds on conditional probabilities with applications in multi-user communication," Z. WahrscheinHchketistheorie u. verw. Geb., vol. 34, pp. 157-177, 1976.
2. T. Berger, Rate Distortion Theory. Englewood Cliffs, NJ: PrenticeHall. 1971.
3. P. Billingsley, Convergence of Probability Measures. New York: Wiley, 1968.
4. I. Csiszér and J. Körner. Information Theory: Coding Theorems for r>\\c.rete. Memoryless Systems. New York: Academic Press, 1981.
5. R. Vf. Gray, Entropy and Information Theory. New York: SpringerVerlag, 1990.
6. R.M. Gray and J. C. Kieffer, "Asymptotically mean stationary measures,'' Annals Probab., vol. 8, pp. 962-973, Oct. 1980.
7. R.M. Gray. Probability, Random Processes, and Ergodic Properties. New York: Springer-Verlag, 1988.
8. R.M. Gray, M. O. Dunham, and R. L. Gobbi, "Ergodicity of Markov channels," IEEE Trans. Inform. Theory, vol. IT-33, no. 5, pp. 656-664, 1987.
9. D.R. Haiverson and G. L. Wise, "Discrete-time detection in φ-mixing noise," IEEE Tram-. Inform. Theory, vol. IT-26, pp. 189-198, 1980.
10. M. losifescu. Finite Markov Processes and Their Applications. New York: Wiley, 1980.
11. J.C. Kieffer and M. Rahe, "Markov channels are asymptotically mean stationary," SIAM J. Math. Anal, vol. 12, no. 3, pp. 293-305, 1981.
12. J.C. Kieffer, "Sample converses in source coding theory," IEEE Trans. Inform. Theory, vol. 37, pp. 263-268, 1991.
13. T. Linder, G. Lugosi, and K. Zcgcr, "Rates of convergence in the source coding theorem, in empirical quantizer design, and in universal lossy source coding," IEEE Trans. Inform. Theory, vol. 40, no. 6, pp. 1728-1740, Nov 1994.
14. K. Marton. "A simple proof of the blowing-up lemma," IEEE Trans. Inform. Theory, vol. IT 32, no. 3, pp. 445-446, 1986.
15. K. Marton and P. Shields, "Ergodic processes and zero divergence," in 1991 IEEE Int. Symp. on Information Theory (Budapest, Hungary, June 23-28, 1991).
16. H.M. H. Shalaby and A. Papamarcou, "Error exponents for distributed detection of Markov sources," IEEE Trans. Inform. Theory, vol. 40, pp. 397-408, 1994.
17. E.-1I. Yang and J. C. Kieffer, "Simple universal lossy data compression schemes derived from Eempel-Ziv algorithm," IEEE Trans. Inform. Theory, vol. 42, no.l, pp. 239-245, Jan. 1996.
18. Z. Zhang and V. K. Wei, "An on-line universal lossy data compression algorithm by continuous codebook refinement-Part I: Basic results," this issue, pp. 803-821.
19. J. Ziv and N. Merhav. "Estimating the number of states of a finite-state source," IEEE Trans. Inform. Theory, vol. 38, no. 1, pp. 61-65, 1992.