On the design of globally optimal communication strategies for real-time noisy communication systems with noisy feedback

IEEE Journal on Selected Areas in Communications

Volumn 26, Issue 4, 2008, Pages 580-595

  Mahajan, Aditya ^a,b   Teneketzis, Demosthenis ^a,b  

^a IEEE

^b The Department of Civil and Environmental Engineering   (United States)

Author keywords

Common belief; Common knowledge; Dynamic teams; Information state; Markov decision processes; Noisy feedback; Real time communication

Indexed keywords

FEEDBACK CONTROL; GLOBAL OPTIMIZATION; MARKOV PROCESSES; REAL TIME SYSTEMS; SPURIOUS SIGNAL NOISE;

INFORMATION STATE; MARKOV DECISION PROCESSES; NOISY FEEDBACK; REAL-TIME COMMUNICATION;

COMMUNICATION SYSTEMS;

EID: 43349086896     PISSN: 07338716     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSAC.2008.080502     Document Type: Article

References (45)

1. C. E. Shannon, "A mathematical theory of communication," Bell System Technical Journal, vol. 22, pp. 379-423, Jul. 1948.
2. P. R. Kumar and P. Varaiya, Stochastic Systems: Estimation Identification and Adaptive Control. Prentice Hall, 1986.
3. H. S. Witsenhausen, "Informational aspects of stochastic control," in Proc. the Oxford Conference on Stochastic Optimization, 1978.
4. D. Teneketzis, "Communication in decentralized control," Ph.D. Thesis, Department of EECS, MIT, Cambridge, MA., Sep. 1979.
5. G. Munson, "Causal information transmission with feedback," Ph.D. Thesis, Department of Electrical Engineering, Cornell University, Ithaca, NY, 1981.
6. A. Gorbunov and P. Pinsker, "Non-anticipatory and prognostic epsilon entropies and message generation rates," Problems in Information Transmission, vol. 9, p. 1840191, 1973.
7. _, "Prognostic epsilon entropy of a Gaussian message and a Gaussian source," Problems in Information Transmission, vol. 10, pp. 184-191, 1974.
8. P. Pinsker and A. Gorbunov, "Epsilon entropy with delay with small mean-square reproduction error," Problems in Information Transmission, vol. 23, no. 2, pp. 3-8, April-June 1987.
9. S. Tatikonda, "Control under communication constraints," Ph.D. Thesis, Department of EECS, Masachussets Institute of Technology, Cambridge, MA, 2000.
10. S. Tatikonda and S. K. Mitter, "Control under communication constraints," IEEE Trans. Automat. Cont., vol. 49, no. 7, pp. 1056-1068, Jul. 2004.
11. N. Merhav and I. Kontoyiannis, "Source coding exponents for zero-delay coding with finite memory," IEEE Trans. Inform. Theory, vol. 49, no. 3, pp. 609-625, 2003.
12. T. Linder and G. Lugosi, "A zero-delay sequential scheme for lossy coding of individual sequences," IEEE Trans. Inform. Theory, vol. 47, no. 6, pp. 2533-2538, 2001.
13. T. Weissman and N. Merhav, "On limited-delay lossy coding and filtering of individual sequences," IEEE Trans. Inform. Theory, vol. 48, no. 3, pp. 721-733, 2002.
14. A. Gyorgy, T. Linder, and G. Lugosi, "Efficient adaptive algorithms and minimax bounds for zero-delay lossy source coding," IEEE Trans. Signal Processing, vol. 52, no. 8, pp. 2337-2347, 2004.
15. S. Matloub and T. Weissman, "Universal zero-delay joint source-channel coding," IEEE Trans. Inform. Theory, vol. 52, no. 12, pp. 5240-5250, Dec. 2006.
16. H. S. Witsenhausen, "On the structure of real-time source coders," Bell System Technical Journal, vol. 58, no. 6, pp. 1437-1451, July-August 1979.
17. V. S. Borkar, S. K. Mitter, and S. Tatikonda, "Optimal sequential vector quantization of Markov sources," SIAM J. Optimal Control, vol. 40, no. 1, pp. 135-148, Jan. 2001.
18. N. T. Gaarder and D. Slepian, "On optimal finite-state digital transmission systems," IEEE Trans. Inform. Theory, vol. 28, no. 2, pp. 167-186, 1982.
19. J. C. Walrand and P. Varaiya, "Optimal causal coding-decoding problems," IEEE Trans. Inform. Theory, vol. 29, no. 6, pp. 814-820, Nov. 1983.
20. R. Lipster and A. Shiryayev, Statistics of Random Processes, Vol. II:Applications. Springer-Verlag, 1977.
21. T. Basar and R. Bansal, "Simultaneous design of measurement channels and control stategies for stochastic systems with feedback," Automatica, vol. 25, pp. 679-694, 1989.
22. _, "Optimal design of measurement channels and control policies for linear-quadratic stochastic systems," European Journal of Operational Research, vol. 93, pp. 226-236, 1994.
23. D. Teneketzis, "On the structure of optimal real-time encoders and decoders in noisy communication," IEEE Trans. Inform. Theory, pp. 4017-4035, Sep. 2006.
24. A. Mahajan and D. Teneketzis, "On jointly optimal encoding, decoding and memory update for noisy real-time communication systems," submitted to IEEE Trans. Inform. Theory, Jan. 2006, available as Control Group Report CGR-06-03, Department of EECS, University of Michigan, Ann Arbor, MI 48109-2122.
25. _, "Fixed delay optimal joint source-channel coding for finite-memory systems," in proceedings of the IEEE International Symposium on Information Theory, Seattle, WA, Jul. 2006, pp. 2319-2323.
26. R. L. Kashyap, "Feedback coding schemes for an additive noise channel with a noisy feedback link," IEEE Trans. Inform. Theory, vol. IT-14, no. 3, pp. 1355-1387, 1968.
27. S. S. Lavenberg, "Feedback communication using orthogonal signals," IEEE Trans. Inform. Theory, vol. IT-15, pp. 478-483, 1969.
28. S. Draper and A. Sahai, "Noisy feedback improves communication reliability," in Proceedings of the IEEE International Symposium on Information Theory, Seattle, WA, July 9-14 2006, pp. 69-73.
29. Y.-H. Kim, A. Lapidoth, and T. Weissman, "The Gaussian channel with noisy feedback," in Proc. IEEE International Symposium on Information Theory, Nice, France, 2007.
30. A. Mahajan and D. Teneketzis, "Optimal performance of feedback control systems with limited communication over noisy channels," submitted to SIAM Journal of Control and Optimization, Dec. 2006, available as Control Group Report CGR-06-07, Department of EECS, University of Michigan, Ann Arbor, MI 48109-2122.
31. _, "Optimal performance of feedback control systems with communcication over noisy channels," in Proc. 45th IEEE Conference of Decision and Control, San Diego, CA, Dec. 2006, pp. 3228-3235.
32. A. Segall, "Stochastic processes in estimation theory," IEEE Trans. Inform. Theory, pp. 275-286, May 1976.
33. H. S. Witsenhausen, "A standard form for sequential stochastic control," Mathematical Systems Theory, vol. 7, no. 1, pp. 5-11, 1973.
34. _, "On information structures, feedback and causality," SIAM J. Control, vol. 9, no. 2, pp. 149-160, May 1971.
35. J. Marschak and R. Radner, Economic Theory of Teams. New Haven: Yale University Press, 1972.
36. Y.-C. Ho, "Team decision theory and information structures," Proc. IEEE, vol. 68, no. 6, pp. 644-654, 1980.
37. H. S. Witsenhausen, "Separation of estimation and control for discrete time systems," Proc. IEEE, vol. 59, no. 11, pp. 1557-1566, Nov. 1971.
38. _, "The intrinsic model for stochastic control: Some open problems," in Lecture Notes in Economics and Mathematical Systems. Springer Verlag, 1975, vol. 107, pp. 322-335.
39. A. Mahajan and D. Teneketzis, "A decision theoretic framework for real-time communications," in Proc. 44th Allerton conference on communication, control and computation, 2005.
40. J. Rust, "Using randomization to break the curse of dimensionality," Econometrica, vol. 65, no. 3, pp. 487-516, 1997.
41. _, "Dealing with the complexity of economic calculations," in Fundamental Limits to Knowledge in Economics. Santa Fe Institute, July 31 - August 3 1996. [Online]. Available: http://econwpa.wustl.edu/eprints/comp/ papers/9610/9610002.abs
42. G. W. Brown, "Iterative solutions of games by ficticius play," in Activity analysis of prodocution and allocation, T. C. Koopmans, Ed. Wiley, 1951, pp. 374-376.
43. N. R. Sandell, Jr., "Control of finite-state, finite-memory stochastic systems," Ph.D. Thesis, Massachussets Institute of Technology, Cambridge, MA., 1974.
44. R. J. Aumann, "Agreeing to disagree," Annals of Statistics, no. 4, pp. 1236-39, 1976.
45. H. S. Witsenhausen, "Some remarks on the concept of state," in Directions in Large-Scale Systems, Y. C. Ho and S. K. Mitter, Eds. Plenum, 1976, pp. 69-75.