Process Definitions of Distortion-Rate Functions and Source Coding Theorems

IEEE Transactions on Information Theory

Volumn 21, Issue 5, 1975, Pages 524-532

  Gray, Robert M ^a   Neuhoff, David L ^a   Omura, Jim K ^b  

^a STANFORD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INFORMATION THEORY;

SOURCE CODING;

CODES, SYMBOLIC;

EID: 0016549555     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/TIT.1975.1055440     Document Type: Article

References (21)

1. C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, pp. 379–423, 623–656, 1948.
2. C. E. Shannon, “Coding theorems for a discrete source with a fidelity criterion,” IRE Nat. Conv. Rec., Part 4, pp. 142–163.
3. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
4. T. Berger, Rate Distortion Theory. Englewood Cliffs, N.J.: Prentice-Hall, 1971.
5. P. Billingsley, Ergodic Theory and Information. New York: Wiley, 1965.
6. H. Chernoff and L. E. Moses, Elementary Decision Theory. New York: Wiley, 1959.
7. A. Khinchine, Mathematical Foundations of Information Theory. New York: Dover, 1957.
8. L. Breiman, “On achieving channel-capacity in finite memory channels,” Ill. J. Math., vol. 4, pp. 246–252.
9. R. M. Gray, D. L. Neuhoff, and P. C. Shields, “A generalization of Ornstein's d distance with applications to information theory,” Ann. Prob., vol. 3, no. 3, Apr. 1975.
10. R. M. Gray, D. L. Neuhoff, and D. S. Ornstein, “Nonblock source coding with a fidelity criterion,” to appear in Ann. Prob., 1975.
11. R. M. Gray and L. D. Davisson “Source coding without the ergodic assumption,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 502–516, July 1974.
12. M. S. Pinsker, Information and Information Stability of Random Variables and Processes. San Francisco, Calif.: Holden-Day, 1964.
13. D. L. Neuhoff, “Source coding and distance measures on random processes,” Ph.D. dissertation, Stanford University, Stanford, Calif., 1974.
14. K. R. Parthasarathy “On the integral representation of the rate of transmission of a stationary channel,” Ill. J. Math., vol. 5, pp. 299–305, 1961.
15. N. Kryloff and N. Bogoliouboff “La théorie générale de la measure dans son application à l'étude des systèmes dynamiques de la mécanique non linéaire,” Ann. Math., vol. 38, no. 2, pp. 65–113, 1937.
16. J. C. Oxtoby “Ergodic sets,” Bull. Amer. Math. Soc., vol. 48, pp. 116–136, 1952.
17. J. K. Omura “A coding theorem for discrete-time sources,” IEEE Trans. Inform. Theory, vol. IT-19, pp. 490–498, July 1973.
18. R. M. Gray and L. D. Davisson “The ergodic decomposition of discrete stationary processes,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 625–636, Sept. 1974.
19. D. S. Ornstein “An application of ergodic theory to probability theory,” Ann. Prob., vol. 1, pp. 43–65, 1973.
20. J. Ziv “Coding of sources with unknown statistics, part II: Distortion relative to a fidelity criterion,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 389–394, May 1972.
21. C. E. Shannon “A note on a partial ordering for communication channels,” Inform. Contr., vol. 1, pp. 390–397, 1958.