On the Asymptotic Tightness of the Shannon Lower Bound

IEEE Transactions on Information Theory

Volumn 40, Issue 6, 1994, Pages 2026-2031

  Zamir, Ram ^b  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Rate distortion theory Shannon lower bound difference distortion measures stationary sources

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; SIGNAL THEORY; VECTOR QUANTIZATION;

DIFFERENCE DISTORTION MEASURES; INFORMATIONAL DIVERGENCE; LINKOV THEORY; RATE DISTORTION THEORY; SHANNON LOWER BOUND; STATIONARY SOURCES;

SIGNAL DISTORTION;

EID: 0028547150     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.340474     Document Type: Article

References (18)

1. C. E. Shannon, “Coding theorems for a discrete source with a fidelity criterion,” IRE Natl. Convention Rec. Part 4, pp. 142-163, 1959.
2. T. Berger, Rate Distortion Theory. Englewood Cliffs, NJ: Prentice-Hall, 1971.
3. Yu. N. Linkov, “Evaluation of epsilon entropy of random variables for small epsilon,” Prob. Inf. Transm., vol. 1, pp. 12-18, 1965.
4. H. Gish and J. N. Pierce, “Asymptotically efficient quantizing,” IEEE Trans. Inform. Theory, vol. IT-14, pp. 676-683, Sept. 1968.
5. A. Gersho, “Asymptotically optimal block quantization,” IEEE Trans. Inform. Theory, vol. IT-25, pp. 373-380, July 1979.
6. Y. Yamada, S. Tazaki, and R. M. Gray, “Asymptotic performance of block quantizers with difference distortion measures,” IEEE Trans. Inform. Theory, vol. IT-26, pp. 6-14, Jan. 1980.
7. J. Binia, M. Zakai, and J. Ziv, “On the e-entropy and the rate-distortion function of certain non-Gaussian processes,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 514-524, July 1974.
8. J. A. Bucklew and G. L. Wise, “Multidimensional asymptotic quantization theory with rth power distortion measures,” IEEE Trans. Inform. Theory, vol. IT-28, pp. 239-247, Mar. 1982.
9. R. Zamir and M. Feder, “On universal quantization by randomized uniform/lattice quantizers,” IEEE Trans. Inform. Theory, vol. 38, pp. 428-436, Mar. 1992.
10. T. Linder and K. Zeger, “Asymptotic entropy constrained performance of tessellating and universal randomized lattice quantization,” IEEE Trans. Inform. Theory, vol. IT 40, pp. 575-579, Mar. 1994.
11. R. M. Gray, Source Coding Theory. Boston: Kluwer, 1990.
12. I. Csiszar, “On an extremum problem of information theory,” Stud. Sci. Math. Hung., pp. 57-70, 1974.
13. A. M. Gerrish and P. M. Schultheiss, “Information rates of non-Gaussian processes,” IEEE Trans. Inform. Theory, vol. IT-10, pp. 1265-271, Oct. 1964.
14. A. R. Barron, “Entropy and the central limit theorem,” Ann. Probab., vol. 14, pp. 336-342, 1986.
15. S. Kullback, Information Theory and Statistics. New York: Wiley, 1959.
16. P. Billingsley, Convergence of Probability Measures. New York: Wiley, 1968.
17. R. L. Wheeden and A. Zygmund, Measure and Integral. New York: Marcel Dekker, 1977.
18. H. Royden, Real Analysis. New York: Macmillan, 1968.