Generalized Network Sharing Outer Bound and the Two-Unicast Problem

We describe a simple improvement over the Network Sharing outer bound for the multiple unicast problem. We call this the Generalized Network Sharing (GNS) outer bound. We note two properties of this bound with regard to the two-unicast problem: a) it is the tightest bound that can be realized using only edge-cut bounds and b) it is tight in the special case when all edges except those from a so-called minimal GNS set have sufficiently large capacities. Finally, we present an example showing that the GNS outer bound is not tight for the two-unicast problem.

[1]  Ness B. Shroff,et al.  Pairwise Intersession Network Coding on Directed Networks , 2010, IEEE Transactions on Information Theory.

[2]  Khaled Ben Letaief,et al.  On the Solvability of 2-pair Unicast Networks --- A Cut-based Characterization , 2010, ArXiv.

[3]  Randall Dougherty,et al.  Linear Network Codes and Systems of Polynomial Equations , 2008, IEEE Transactions on Information Theory.

[4]  Alex J. Grant,et al.  Mission impossible: Computing the network coding capacity region , 2008, 2008 IEEE International Symposium on Information Theory.

[5]  Randall Dougherty,et al.  Networks, Matroids, and Non-Shannon Information Inequalities , 2007, IEEE Transactions on Information Theory.

[6]  Zhen Zhang,et al.  An outer bound for multisource multisink network coding with minimum cost consideration , 2006, TNET.

[7]  Serap A. Savari,et al.  Edge-Cut Bounds on Network Coding Rates , 2006, Journal of Network and Systems Management.

[8]  Insufficiency of linear coding in network information flow , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[9]  R. Koetter,et al.  An algebraic approach to network coding , 2001, Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252).

[10]  Rudolf Ahlswede,et al.  Network information flow , 2000, IEEE Trans. Inf. Theory.

[11]  Zhen Zhang,et al.  Distributed Source Coding for Satellite Communications , 1999, IEEE Trans. Inf. Theory.

[12]  R. Yeung,et al.  On characterization of entropy function via information inequalities , 1998, Proceedings. 1998 IEEE International Symposium on Information Theory (Cat. No.98CH36252).

[13]  Peter Elias,et al.  A note on the maximum flow through a network , 1956, IRE Trans. Inf. Theory.