A theory of network equivalence - Part I: Point-to-point channels

IEEE Transactions on Information Theory

Volumn 57, Issue 2, 2011, Pages 972-995

  Koetter, Ralf ^a   Effros, Michelle ^b   Medard, Muriel ^c  

^a TECHNICAL UNIVERSITY OF MUNICH   (Germany)

^b California Institute of Technology   (United States)

^c USA   (United States)

Author keywords

Capacity; component models; equivalence; network coding

Indexed keywords

ACYCLIC NETWORKS; CAPACITY; CAPACITY REGIONS; CHANNEL'S CAPACITY; COMPONENT MODEL; EQUIVALENCE; MEMORYLESS; MULTICAST CONNECTIONS; MULTICASTS; NETWORK CAPACITY; NETWORK CODING;

INFORMATION THEORY; PIPE;

MULTICASTING;

EID: 79251504248     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2102110     Document Type: Article

References (23)

1. R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeung, "Network information flow," IEEE Trans. Inf. Theory, vol. IT-46, pp. 1204-1216, Jul. 2000.
2. A. R. Lehman and E. Lehman, "Complexity classifications of network information flow problems," in Allerton Conf. on Communications, Control, and Computing, Monticello, IL, Sep. 2003.
3. T. Chan and A. Grant, "Dualities between entropy functions and network codes," IEEE Trans. Inf. Theory, vol. 54, pp. 4470-4487, Oct. 2008.
4. L. Song, R. W. Yeung, and N. Cai, "Zero-error network coding for acyclic networks," IEEE Trans. Inf. Theory, vol. 49, pp. 3129-3139, Jul. 2003.
5. N. Harvey, R. Kleinberg, and A. R. Lehman, "On the capacity of information networks," IEEE Trans. Inf. Theory, vol. 52, pp. 2345-2364, Jun. 2006. (Pubitemid 43898896)
6. A. Subramanian and A. Thangaraj, "A simple algebraic formulation for the scalar linear network coding problem," ArXiv e-Prints, Jul. 2008.
7. S. Borade, "Network information flow: Limits and achievability," in Proc. 2002 IEEE Int. Symp. Information Theory, Jul. 2002, p. 139.
8. R. Koetter and M. Médard, "An algebraic approach to network coding," IEEE/ACM Trans. Netw., vol. 11, pp. 782-795, Oct. 2003.
9. N. Harvey and R. Kleinberg, "Tighter cut-set bounds for -pairs communication problems," in Proc. Allerton Conf. Communication, Control, and Computing, Monticello, IL, Sep. 2005.
10. G. Kramer and S. Savari, "Capacity bounds for relay networks," in Information Theory and Applications Workshop, San Diego, CA, Jan. 2006.
11. G. Kramer and S. Savari, "Edge-cut bounds on network coding rates," J. Netw. Syst. Manag., vol. 14, pp. 49-67, Mar. 2006.
12. A. Avestimehr, S. Diggavi, and D. Tse, "Approximate capacity of Gaussian relay networks," in Proc. 2008 IEEE Int. Symp. Information Theory, Jul. 2008, pp. 474-478.
13. C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., vol. 27, pp. 379-423, 1948.
14. R. Ahlswede, "Multi-way communication channels," in Proc. 2nd. Int. Symp. Information Theory, Tsahkadsor, Armenia, 1971, pp. 23-52.
15. H. Liao, "Multiple Access Channels," Ph. D. dissertation, Dept. Elect. Eng., Univ. Hawaii, Honolulu, 1972.
16. T. M. Cover, "Broadcast channels," IEEE Trans. Inf. Theory, vol. IT-18, pp. 2-14, Jan. 1972.
17. L. Song, R. W. Yeung, and N. Cai, "A separation theorem for single-source network coding," IEEE Trans. Inf. Theory, vol. 52, pp. 1861-1871, May 2006.
18. T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. Hoboken, NJ: Wiley, 2006.
19. R. G. Gallager, Information Theory and Reliable Communication. New York: Wiley, 1968.
20. C. Bennett, P. Shor, J. Smolin, and A. Thapliyal, "Entanglement- assisted capacity of a quantum channel and the reverse Shannon theorem," IEEE Trans. Inf. Theory, vol. 48, pp. 2637-2655, Oct. 2002.
21. W.-H. Gu and M. Effros, "A strong converse for a collection of network source coding problems," in Proc. 2009 IEEE Int. Symp. Information Theory, Seoul, Korea, Jun. 2009, pp. 2316-2320.
22. W.-H. Gu, "On Achievable Rate Regions for Source Coding Networks," Ph.D. dissertation, Cal. Inst. Technol., Pasadena, CA, 2009.
23. U. Madhow, Fundamentals of Digital Communication. Cambridge, U.K.: Cambridge Univ. Press, 1998.