TY - GEN

T1 - Network Coding Solutions for the Combination Network and its Subgraphs

AU - Cai, Han

AU - Etzion, Tuvi

AU - Schwartz, Moshe

AU - Wachter-Zeh, Antonia

N1 - Funding Information:
We Thank Yiwei Zhang for helpful discussions. A. Wachter- Zeh and M. Schwartz were supported by a German Israeli Project Cooperation (DIP) grant under grant no. PE2398/1-1 and KR3517/9-1.
Funding Information:
3) Can vector gaps for multicast networks with two mes-sages be larger than the one obtained for minimal multicast networks? 4) What is the largest possible vector gap as a function of h and t for a multicast network with h messages? ACKNOWLEDGMENT We Thank Yiwei Zhang for helpful discussions. A. Wachter-Zeh and M. Schwartz were supported by a German Israeli Project Cooperation (DIP) grant under grant no. PE2398/1-1 and KR3517/9-1.
Publisher Copyright:
© 2019 IEEE.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85073168035&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2019.8849620

DO - 10.1109/ISIT.2019.8849620

M3 - Conference contribution

AN - SCOPUS:85073168035

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 862

EP - 866

BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings

PB - Institute of Electrical and Electronics Engineers

T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019

Y2 - 7 July 2019 through 12 July 2019

ER -