Network Coding Solutions for the Combination Network and its Subgraphs

Han Cai; Tuvi Etzion; Moshe Schwartz; Antonia Wachter-Zeh

doi:10.1109/ISIT.2019.8849620

Network Coding Solutions for the Combination Network and its Subgraphs

Han Cai, Tuvi Etzion, Moshe Schwartz, Antonia Wachter-Zeh

Department of Electrical & Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

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.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers
Pages	862-866
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849620
State	Published - 1 Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July
ISSN (Print)	2157-8095

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Modeling and Simulation
Applied Mathematics

Access to Document

10.1109/ISIT.2019.8849620

Cite this

Cai, H., Etzion, T., Schwartz, M., & Wachter-Zeh, A. (2019). Network Coding Solutions for the Combination Network and its Subgraphs. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 862-866). Article 8849620 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ISIT.2019.8849620

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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.",

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Cai, H, Etzion, T, Schwartz, M & Wachter-Zeh, A 2019, Network Coding Solutions for the Combination Network and its Subgraphs. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849620, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers, pp. 862-866, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849620

Network Coding Solutions for the Combination Network and its Subgraphs. / Cai, Han; Etzion, Tuvi; Schwartz, Moshe et al.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers, 2019. p. 862-866 8849620 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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Cai H, Etzion T, Schwartz M, Wachter-Zeh A. Network Coding Solutions for the Combination Network and its Subgraphs. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers. 2019. p. 862-866. 8849620. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT.2019.8849620

Network Coding Solutions for the Combination Network and its Subgraphs

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