On the index coding problem and its relation to network coding and matroid theory

IEEE Transactions on Information Theory

Volumn 56, Issue 7, 2010, Pages 3187-3195

  El Rouayheb, Salim ^a   Sprintson, Alex ^a   Georghiades, Costas ^a  

^a Texas AandM University   (United States)

Author keywords

Index coding; Matroid theory; Network coding; Nonlinear codes; Side information

Indexed keywords

CODING PROBLEMS; COMMUNICATION CHANNEL; ENCODING SCHEMES; GENERAL NETWORKS; INFORMATION MESSAGES; LINEAR CODES; LINEAR REPRESENTATION; MATROID REPRESENTATION; MATROID THEORY; MATROIDS; NETWORK CODING; NONLINEAR CODES; OPTIMUM NUMBER; RESEARCH COMMUNITIES; SIDE INFORMATION;

AD HOC NETWORKS; ENCODING (SYMBOLS); MATRIX ALGEBRA; SIGNAL RECEIVERS; WIRELESS AD HOC NETWORKS;

INFORMATION THEORY;

EID: 77953735305     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2048502     Document Type: Article

References (27)

1. S. Katti, H. Rahul, W. Hu, D. Katabi, M. Medard, and J. Crowcroft, "XORs in the Air: Practical Wireless Network Coding," in Proc. 2006 Conf. Appl., Technol., Architect. Protocols for Comput. Commun. SIGCOMM' 06, New York, 2006, pp. 243-254. (Pubitemid 44623731)
2. S. Katti, D. Katabi, H. Balakrishnan, and M. Medard, "Symbol-level network coding for wireless mesh networks," in Proc. ACM SIGCOMM, Seattle, WA, 2008.
3. Y. Birk and T. Kol, "Coding-on-demand by an informed source (ISCOD) for efficient broadcast of different supplemental data to caching clients," IEEE Trans. Inf. Theory, vol.52, no.6, pp. 2825-2830, Jun. 2006.
4. H. S. Witsenhausen, "The zero-error side information problem and chromatic numbers," IEEE Trans. Inf. Theory, vol.IT-22, no.5, pp. 592-593, 1976.
5. G. Simonyi, "OnWitsenhausen's zero-error rate for multiple sources," IEEE Trans. Inf. Theory, vol.49, no.12, pp. 3258-3261, Dec. 2003.
6. Z. Bar-Yossef, Y. Birk, T. S. Jayram, and T. Ko, "Index coding with side information," in Proc. 47th Ann. IEEE Symp. Found. Comput. Sci. (FOCS), 2006, pp. 197-206.
7. R. Peeters, "Orthogonal representations over finite fields and the chromatic number of graphs," Combinatorica, vol.16, no.3, pp. 417-431, 1996. (Pubitemid 126353017)
8. E. Lubetzky and U. Stav, "Nonlinear index coding outperforming the linear optimum," in Proc. 48th Ann. IEEE Symp. Found. Comput. Sci. (FOCS), 2007, pp. 161-167.
9. N. Alon, E. Lubetzky, U. Stav, A.Weinstein, and A. Hasidim, "Broadcasting with side information," in Proc. 49th Ann. IEEE Symp. Found. Comput. Sci. (FOCS), Philadelphia, PA, Oct. 2008, pp. 823-832.
10. Y. Wu, J. Padhye, R. Chandra, V. Padmanabhan, and P. A. Chou, "The local mixing problem," in Proc. Inf. Theory Appl. Workshop, San Diego, CA, Feb. 2006.
11. M. Langberg and A. Sprintson, "On the hardness of approximating the network coding capacity," in Proc. ISIT, Toronto, ON, Canada, Jun. 2008, 2008.
12. S. El Rouayheb, M. A. R. Chaudhry, and A. Sprintson, "On the minimum number of transmissions in single-hop wireless coding networks," in Proc. IEEE Inf. Theory Workshop, Lake Tahoe, NV, 2007.
13. M. A. R. Chaudhry and A. Sprintson, "Efficient algorithms for index coding," in Infocom'08 Student Workshop, 2008.
14. R. Ahlswede, N. Cai, S.-Y. R. Li, and R. W. Yeung, "Network information flow," IEEE Trans. Inf. Theory, vol.46, no.4, pp. 1204-1216, Apr. 2000.
15. S.-Y. R. Li, R. W. Yeung, and N. Cai, "Linear network coding," IEEE Trans. Inf. Theory, vol.49, no.2, pp. 371-381, Feb. 2003.
16. R. Koetter and M. Medard, "An algebraic approach to network coding," IEEE/ACM Trans. Netw., vol.11, no.5, pp. 782-795, 2003.
17. T. Ho, R. Koetter,M. Medard, D. Karger, and M. Effros, "The benefits of coding over routing in a randomized setting," in Proc. IEEE Int. Symp. Inf. Theory, 2003.
18. S. Jaggi, P. Sanders, P. A. Chou, M. Effros, S. Egner, K. Jain, and L. M. G. M. Tolhuizen, "Polynomial time algorithms for multicast network code construction," IEEE Trans. Inf. Theory, vol.51, no.6, pp. 1973-1982, Jun. 2005.
19. C. Fragouli and E. Soljanin, Network Coding Fundamentals (Foundations and Trends in Networking). New York: Now, 2007.
20. R. Yeung, S.-Y. Li, and N. Cai, Network Coding Theory (Foundations and Trends in Communications and Information Theory). New York: Now , 2006.
21. R. Dougherty, C. Freiling, and K. Zeger, "Insufficiency of linear coding in network information flow," IEEE Trans. Inf. Theory, vol.51, no.8, pp. 2745-2759, 2005. (Pubitemid 41158597)
22. J. G. Oxley, Matroid Theory. New York: Oxford Univ. Press , Jan. 1993.
23. D. J. A. Welsh, Matroid Theory. London, U.K.: Academic, 1976.
24. J. Simonis and A. Ashikhmin, "Almost affine codes," Desings, Codes Cryptogr., vol.14, pp. 179-797, 1998.
25. F. Matús, "Matroid representations by partitions," Discrete Math., vol.203, pp. 169-194, 1999.
26. M. Medard, M. Effros, T. Ho, and D. R. Karger, "On coding for nonmulticast networks," in Proc. 41st Ann. Allerton Conf. Commun., Control, Comput., Oct. 2003.
27. R. Dougherty, C. Freiling, and K. Zeger, "Networks, matroids, and non- Shannon information inequalities," IEEE Trans. Inf. Theory, vol.53, no.6, Jun. 2007.