Sum-networks: Dependency on Characteristic of the Finite Field under Linear Network Coding
作者： Brijesh Kumar Rai , Niladri Das
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摘要: Sum-networks are networks where all the terminals demand sum of symbols generated at sources. It has been shown that for any finite set/co-finite set prime numbers, there exists a sum-network which vector linear solution if and only characteristic field belongs to given set. also positive rational number $k/n$, capacity equal $k/n$. is natural question whether, primes $\{p_1,p_2,\ldots,p_l\}$, achieving rate $k/n$ fractional network coding We show indeed such by constructing sum-network.
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Niladri Das, Brijesh Kumar Rai, On the number of sources and terminals of sum-networks with capacity p/q national conference on communications. pp. 1- 6 ,(2015) , 10.1109/NCC.2015.7084914
Brijesh Kumar Rai, Bikash Kumar Dey, On Network Coding for Sum-Networks IEEE Transactions on Information Theory. ,vol. 58, pp. 50- 63 ,(2012) , 10.1109/TIT.2011.2169532
Ardhendu Tripathy, Aditya Ramamoorthy, Sum-networks from undirected graphs: Construction and capacity analysis allerton conference on communication, control, and computing. pp. 651- 658 ,(2014) , 10.1109/ALLERTON.2014.7028517
Brijesh Kumar Rai, Niladri Das, Sum-Networks: Min-Cut = 2 Does Not Guarantee Solvability IEEE Communications Letters. ,vol. 17, pp. 2144- 2147 ,(2013) , 10.1109/LCOMM.2013.101413.131605
Michael Langberg, Aditya Ramamoorthy, Communicating the sum of sources in a 3-sources/3-terminals network international symposium on information theory. pp. 2121- 2125 ,(2009) , 10.1109/ISIT.2009.5205758
R. Dougherty, C. Freiling, K. Zeger, Insufficiency of linear coding in network information flow IEEE Transactions on Information Theory. ,vol. 51, pp. 2745- 2759 ,(2005) , 10.1109/TIT.2005.851744
S.-Y.R. Li, R.W. Yeung, Ning Cai, Linear network coding IEEE Transactions on Information Theory. ,vol. 49, pp. 371- 381 ,(2003) , 10.1109/TIT.2002.807285
S. Jaggi, P. Sanders, P.A. Chou, M. Effros, S. Egner, K. Jain, L.M.G.M. Tolhuizen, Polynomial time algorithms for multicast network code construction IEEE Transactions on Information Theory. ,vol. 51, pp. 1973- 1982 ,(2005) , 10.1109/TIT.2005.847712
Aditya Ramamoorthy, Michael Langberg, Communicating the Sum of Sources Over a Network IEEE Journal on Selected Areas in Communications. ,vol. 31, pp. 655- 665 ,(2013) , 10.1109/JSAC.2013.130404
R. Koetter, M. Medard, An algebraic approach to network coding IEEE ACM Transactions on Networking. ,vol. 11, pp. 782- 795 ,(2003) , 10.1109/TNET.2003.818197