On network coding for sum-networks

IEEE Transactions on Information Theory

Volumn 58, Issue 1, 2012, Pages 50-63

  Rai, Brijesh Kumar ^a,b   Dey, Bikash Kumar ^b  

^a INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

Function computation; linear network coding; network coding; polynomial equations; solvability

Indexed keywords

ACYCLIC NETWORKS; FINITE FIELDS; INTEGER COEFFICIENT; LINEAR SOLUTION; POLYNOMIAL EQUATIONS; PRIME NUMBER; SOLVABILITY;

CODES (SYMBOLS); COMMUNICATION; LINEAR NETWORKS; POLYNOMIALS; TELECOMMUNICATION NETWORKS;

NETWORK CODING;

EID: 84855691827     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2011.2169532     Document Type: Article

References (38)

1. 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, 2000.
2. S.-Y. R. Li, R. W. Yeung, and N. Cai, "Linear network coding," IEEE Trans. Inf. Theory, vol. 49, no. 2, pp. 371-381, 2003.
3. R.Koetter andM. Médard, "An algebraic approach to network coding," IEEE/ACM Trans. Netw., vol. 11, no. 5, pp. 782-795, 2003.
4. S. Jaggi, P. Sanders, P. A. Chou, M. Effros, S. Egner, K. Jain, and L. Tolhuizen, "Polynomial time algorithms for multicast network code construction," IEEE Trans. Inf. Theory, vol. 51, no. 6, pp. 1973-1982, 2005. (Pubitemid 40843620)
5. T. Ho, R. Koetter, M. Médard, M. Effros, J. Shi, and D. Karger, "A random linear network coding approach to multicast," IEEE Trans. Inf. Theory, vol. 52, no. 10, pp. 4413-4430, 2006. (Pubitemid 46445282)
6. A. R. Lehman and E. Lehman, "Complexity classification of network information flow problems," in Proc. 41st Ann. Allerton Conf. Commun., Contr., Comput., Monticello, IL, Oct. 2003.
7. M. Langberg and A. Sprintson, "On the hardness of approximating the network coding capacity," in Proc. ISIT, Toronto, Canada, 2008.
8. M. Médard,M. Effros, T. Ho, and D. Karger, "On coding for nonmulticast networks," in Proc. 41st Ann. Allerton Conf. Commun., Contr., Comput., Monticello, IL, Oct. 2003.
9. S. Riis, "Linear versus nonlinear boolean functions in network flow," in Proc. 38th Ann. Conf. Inf. Sci. Syst., Princeton, NJ, Mar. 2004.
10. 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)
11. R. Dougherty, C. Freiling, and K. Zeger, "Linear network codes and systems of polynomial equations," IEEE Trans. Inf. Theory, vol. 54, no. 5, pp. 2303-2316, 2008. (Pubitemid 351689561)
12. R. Dougherty and K. Zeger, "Nonreversibility and equivalent constructions of multiple-unicast networks," IEEE Trans. Inf. Theory, vol. 52, no. 11, pp. 5067-5077, 2006. (Pubitemid 44680592)
13. R.Koetter,M. Effros, T. Ho, andM. Médard, "Network codes as codes on graphs," in Proc. CISS, 2004.
14. S. Riis, "Reversible and irreversible information networks," IEEE Trans. Inf. Theory, vol. 53, no. 11, pp. 4339-4349, 2007. (Pubitemid 350141930)
15. J. Korner and K. Marton, "How to encode the modulo-two sum of binary sources," IEEE Trans. Inf. Theory, vol. 25, no. 2, pp. 219-221, 1979. (Pubitemid 9443306)
16. D. Krithivasan and S. S. Pradhan, "An achievable rate region for distributed source coding with reconstruction of an arbitrary function of the sources," in Proc. ISIT, Toronto, Canada, 2008.
17. R. G. Gallager, "Finding parity in a simple broadcast network," IEEE Trans. Inf. Theory, vol. 34, pp. 176-180, 1988.
18. A. Ramamoorthy, "Communicating the sum of sources over a network," in Proc. ISIT, Toronto, Canada, 2008, pp. 1646-1650.
19. M. Langberg and A. Ramamoorthy, "Communicating the sum of sources in a 3-sources/3-terminals network," in Proc. ISIT, Seoul, Korea, 2009.
20. R. Appuswamy, M. Franceschetti, N. Karamchandani, and K. Zeger, "Network computing capacity for the reverse butterfly network," in Proc. ISIT, Seoul, Korea, 2009.
21. R. Appuswamy, M. Franceschetti, N. Karamchandani, and K. Zeger, "Network coding for computing," inProc. Ann. AllertonConf., IIlinois, 2008.
22. M. Langberg and A. Ramamoorthy, "Communicating the sum of sources in a 3-sources/3-terminals network; revisited," in Proc. ISIT, 2010.
23. A. Ramamoorthy and M. Langberg, Communicating the Sum of Sources over a Network 2010[Online]. Available: http://arxiv.org/abs/1001.5319
24. S. Shenvi and B. K. Dey, "A necessary and sufficient condition for solvability of a 3s/3t sum-network," in Proc. ISIT, Austin, TX, Jun. 2010.
25. S. Shenvi and B. K. Dey, On the Solvability of 3-Source 3-Terminal Sum-Networks[Online]. Available: http://arxiv.org/abs/1001.4137
26. R. Appuswamy, M. Franceschetti, N. Karamchandani, and K. Zeger, Network Coding for Computing Part I : Cut-Set Bounds[Online]. Available: http://arxiv.org/abs/0912.2820
27. T. S. Han and K. Kobayashi, "A dichotomy of functions of correlated sources ," IEEE Trans. Inf. Theory, vol. 33, no. 1, pp. 69-86, 1987.
28. A. Orlitsky and J. R. Roche, "Coding for computing," IEEE Trans. Inf. Theory, vol. 47, no. 3, pp. 903-917, 2001. (Pubitemid 32425425)
29. H. Feng, M. Effros, and S. A. Savari, "Functional source coding for networks with receiver side information," in Proc. Allerton Conf. Commun., Contr., Comput., Sep. 2004.
30. J. N. Tsistsiklis, "Decentralized detection by a large number of sensors," Math. Contr., Signals Syst., vol. 1, no. 2, pp. 167-182, 1988.
31. A. Giridhar and P. R. Kumar, "Computing and communicating functions over sensor networks," IEEE J. Sel. Areas Commun., vol. 23, no. 4, pp. 755-764, 2005. (Pubitemid 40519630)
32. Y. Kanoria and D. Manjunath, "On distributed computation in noisy random planar networks," in Proc. ISIT, Nice, France, 2008.
33. S. Boyd, A. Ghosh, B. Prabhaar, and D. Shah, "Gossip algorithms: Design, analysis and applications," in Proc. IEEE INFOCOM, Miami, FL, 2005.
34. R. Dougherty, C. Freiling, and K. Zeger, "Unachievability of network coding capacity," IEEE Trans. Inf. Theory, vol. 52, no. 6, pp. 2365-2372, 2006. (Pubitemid 43898897)
35. M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra. Reading, MA: Addison-Wesley, 1969.
36. S. Jaggi, M. Effros, T.Ho, andM.Médard, "On linear network coding," in Proc. 42st Ann. Allerton Conf. Commun., Contr., Comput., IL, Oct. 2006.
37. A. Ramamoorthy and M. Langberg, Pers. Commun. 2008.
38. J. Cannons, R. Dougherty, C. Freiling, and K. Zeger, "Network routing capacity," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 777-788, 2006. (Pubitemid 46444873)