Network coding theory part II: multiple source
Communications and Information Theory
Network coding theory: single sources
Communications and Information Theory
Secret Sharing and Non-Shannon Information Inequalities
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
ICUFN'09 Proceedings of the first international conference on Ubiquitous and future networks
A new construction method for networks from matroids
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
A recursive construction of the set of binary entropy vectors
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Matroids can be far from ideal secret sharing
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Information inequalities for joint distributions, with interpretations and applications
IEEE Transactions on Information Theory
On the index coding problem and its relation to network coding and matroid theory
IEEE Transactions on Information Theory
Size and Treewidth Bounds for Conjunctive Queries
Journal of the ACM (JACM)
Constructing rate 1/p systematic binary quasi-cyclic codes based on the matroid theory
Designs, Codes and Cryptography
| Hi-index | 754.96 |
We define a class of networks, called matroidal networks, which includes as special cases all scalar-linearly solvable networks, and in particular solvable multicast networks. We then present a method for constructing matroidal networks from known matroids. We specifically construct networks that play an important role in proving results in the literature, such as the insufficiency of linear network coding and the unachievability of network coding capacity. We also construct a new network, from the Vamos matroid, which we call the Vamos network, and use it to prove that Shannon-type information inequalities are in general not sufficient for computing network coding capacities. To accomplish this, we obtain a capacity upper bound for the Vamos network using a non-Shannon-type information inequality discovered in 1998 by Zhang and Yeung, and then show that it is smaller than any such bound derived from Shannon-type information inequalities. This is the first application of a non-Shannon-type inequality to network coding. We also compute the exact routing capacity and linear coding capacity of the Vamos network. Finally, using a variation of the Vamos network, we prove that Shannon-type information inequalities are insufficient even for computing network coding capacities of multiple-unicast networks.