Zero-rate feedback can achieve the empirical capacity

IEEE Transactions on Information Theory

Volumn 56, Issue 1, 2010, Pages 25-39

  Eswaran, Krishnan ^a   Sarwate, Anand D ^a,b   Sahai, Anant ^a   Gastpar, Michael C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of California at San Diego   (United States)

Author keywords

Arbitrarily varying channels; Common randomness; Feedback communication; Hybrid ARQ; Individual sequences; Rateless codes; Universal communication

Indexed keywords

COMMON RANDOMNESS; FEEDBACK COMMUNICATIONS; HYBRID ARQ; INDIVIDUAL SEQUENCES; RATELESS CODES;

COMMUNICATION; INTERFERENCE SUPPRESSION;

FEEDBACK;

EID: 73849132814     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2009.2034779     Document Type: Article

References (39)

1. K. Eswaran, A. Sarwate, A. Sahai, and M. Gastpar, "Binary additive channels with individual noise sequences and limited active feedback," in Proc. IEEE Int. Symp. Information Theory (ISIT), Nice, France, Jun. 2007.
2. S. Draper, B. Frey, and F. Kschischang, "Rateless coding for non-ergodic channels with decoder channel state information," IEEE Trans. Inf. Theory, vol. 55, no. 9, pp. 4119-4133, Sep. 2009.
3. O. Shayevitz and M. Feder, "Achieving the empirical capacity using feedback: Memoryless additive models," IEEE Trans. Inf. Theory, vol. 55, no. 3, pp. 1269-1295, Mar. 2009.
4. A. Sahai, "Why block-length and delay behave differently if feedback is present?," IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 1860-1886, May 2008.
5. A. Sahai and S. Draper, "Beating the Burnashev bound using noisy feedback," in Proc. 44th Allerton Conf. Communication, Control, and Computing, Monticello, IL, Sept. 2006, pp. 421-430.
6. A. Sahai, "Balancing forward and feedback error correction for erasure channels with unreliable feedback," IEEE Trans. Inf. Theory, submitted for publication.
7. E. Soljanin, R. Liu, and P. Spasojevic, "Hybrid ARQ with random transmission assignments," in Advances in Network Information Theory, , ser. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, P. Gupta, G. Kramer, and A. J. van Wijngaarden, Eds. Providence, RI: AMS, 2004.
8. M. Horstein, "Sequential transmission using noiseless feedback," IEEE Trans. Inf. Theory, vol. IT-9, no. 3, pp. 136-143, Jul. 1963.
9. J. P. M. Schalkwijk and T. Kailath, "A coding scheme for additive noise channels with feedback I: No bandwidth constraint," IEEE Trans. Inf. Theory, vol. IT-9, no. 3, pp. 172-182, Jul. 1966.
10. M. Burnashev, "Data transmission over a discrete channel with feedback, random transmission time," Probl. Inf. Transm., vol. 12, no. 4, pp. 250-265, Oct.-Dec. 1976.
11. T. Cover and S. Pombra, "Gaussian feedback capacity," IEEE Trans. Inf. Theory, vol. 35, no. 1, pp. 37-43, Jan. 1989.
12. J. Ooi and G. Wornell, "Fast iterative coding techniques for feedback channels," IEEE Trans. Inf. Theory, vol. 44, no. 7, pp. 2960-2976, Nov. 1998.
13. J. Ooi, Coding for Channels With Feedback. Boston, MA: Kluwer Academic, 1998.
14. Y.-H. Kim, "Feedback capacity of stationary Gaussian channels," IEEE Trans. Inf. Theory 2006 [Online]. Available: http://arxiv.org/abs/cs.IT/ 0602091, submitted for publication.
15. S. Draper and A. Sahai, "Variable-length channel coding with noisy feedback," Europ. Trans. Telecommun., vol. 19, no. 4, pp. 355-370, Apr. 2008.
16. M. Gastpar and G. Kramer, "On noisy feedback for interference channels," in Proc. 40th Asilomar Conf. Signals, Systems, and Computers, Pacific Grove, CA, 2006, pp. 216-220.
17. M. Wigger, "Noisy feedback is strictly better than no feedback on the Gaussian MAC," in Proc. 2006 Kailath Symp., Stanford, CA, Jul. 2006.
18. A. Lapidoth and M. A.Wigger, "On the Gaussian MAC with imperfect feedback," IEEE Trans. Inf. Theory, to be published.
19. Y.-H. Kim, A. Lapidoth, and T.Weissman, "On reliability of Gaussian channels with noisy feedback," in Proc. 44th Allerton Conf. Communication, Control, and Computing, Monticello, IL, Sep. 2006, pp. 364-371.
20. M. Luby, "LT codes," in Proc. 43rd Annu. IEEE Symp. Foundations of Computer Science, Vancouver, BC, 2002, pp. 271-280.
21. A. Shokrollahi, "Fountain codes," in Proc. 41st Allerton Conf. Communication, Control, and Computing, Monticello, IL, Oct. 2003, pp. 1290-1297.
22. N. Shulman, "Communication Over an Unknown Channel Via Common Broadcasting," Ph.D. dissertation, Tel-Aviv University, Tel-Aviv, Israel, 2003.
23. S. Draper, B. Frey, and F. Kschischang, "Efficient variable length channel coding for unknown DMCs," in Proc. IEEE Int. Symp. Information Theory, Chicago, IL, Jun./Jul. 2004, p. 379.
24. A. Tchamkerten and İ. E. Telatar, "Variable length coding over an unknown channel," IEEE Trans. Inf. Theory, vol. 52, no. 5, pp. 2126-2145, May 2006.
25. N. Shulman and M. Feder, "The uniform distribution as a uniform prior," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1356-1362, Jun. 2004.
26. I. Csiszár and J. Körner, Information Theory: Coding Theorems for Discrete Memoryless Systems. Budapest, Hungary: Akadémi Kiadó, 1982.
27. A. Sahai and S. Mitter, "The necessity and sufficiency of anytime capacity for control over a noisy communication link: Part I," IEEE Trans. Inf. Theory, vol. 52, no. 8, pp. 3369-3395, Aug. 2006.
28. W. Hoeffding, "Probability inequalities for sums of bounded random variables," J. Amer. Statist. Assoc., vol. 58, no. 1, pp. 13-30, Mar. 1963.
29. B. Hughes and T. Thomas, "On error exponents for arbitrarily varying channels," IEEE Trans. Inf. Theory, vol. 42, no. 1, pp. 87-98, Jan. 1996.
30. L. Schwartz, "Feedback for error control and two-way communication," IEEE Trans. Commun. Syst., vol. COM-11, no. 1, pp. 49-56, Mar. 1963.
31. J. Hayes, "Adaptive feedback communications," IEEE Trans. Commun. Technol., vol. COM-16, no. 1, pp. 29-34, Feb. 1968.
32. N. Ahmed, M. Khojastepour, A. Sabharwal, and B. Aazhang, "Outage minimization with limited feedback for the fading relay channel," IEEE Trans. Commun., vol. 54, no. 4, pp. 659-669, Apr. 2006.
33. D. Love, R. Heath, Jr., V. Lau, D. Gesbert, B. Rao, and M. Andrews, "An overview of limited feedback in wireless communication systems," IEEE J. Sel. Areas Commun., vol. 26, no. 8, pp. 1341-1365, Oct. 2008.
34. R. Ahlswede, "Elimination of correlation in random codes for arbitrarily varying channels," Z.Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 44, no. 2, pp. 159-175, 1978.
35. A. Sarwate and M. Gastpar, "Rateless codes for AVC models," IEEE Trans. Inf. Theory, to be published.
36. N. Merhav and N. Feder, "Universal prediction," IEEE Trans. Inf. Theory, vol. 44, no. 6, pp. 2124-2147, Oct. 1998.
37. Y. Lomnitz and M. Feder, "Feedback communication over individual channels," in Proc. 2009 Int. Symp. Information Theory, Seoul, Korea, Jul. 2009.
38. S. Kozat and A. Singer, "Universal switching linear least squares prediction," in Proc. 2006 Information Theory and Its Applications Workshop, La Jolla, CA, Feb. 2006 [Online]. Available: http://ita.ucsd.edu/ workshop/06/talks/papers/143.pdf.
39. M. Feder, "Achieving the empirical capacity of individual noise channels using feedback," in Proc. 2006 Kailath Symp., Stanford, CA, Jul. 2006.