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Network Coding Solutions for the Combination...
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Network Coding Solutions for the Combination Network and its Subgraphs

Abstract

The combination network is one of the simplest and insightful networks in coding theory. The vector network coding solutions for this network and some of its sub-networks are examined. For a fixed alphabet size of a vector network coding solution, an upper bound on the number of nodes in the network is obtained. This bound is an MDS bound for subspaces over a finite field. A family of sub-networks of combination networks is defined. It is proved that for this family of networks, which are minimal multicast networks, there is a gap in the minimum alphabet size between vector network coding solutions and scalar network coding solutions. This gap is obtained for any number of messages and is based on coloring of the q-Kneser graph and a new hypergraph generalization for it.

Authors

Cai H; Etzion T; Schwartz M; Wachter-Zeh A

Volume

00

Pagination

pp. 862-866

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Publication Date

July 12, 2019

DOI

10.1109/isit.2019.8849620

Name of conference

2019 IEEE International Symposium on Information Theory (ISIT)
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