On the Gap between Scalar and Vector Solutions of Generalized Combination Networks

Hedongliang Liu, Hengjia Wei, Sven Puchinger, Antonia Wachter-Zeh, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review

Abstract

We study scalar-linear and vector-linear solutions of the generalized combination network. We derive new upper and lower bounds on the maximum number of nodes in the middle layer, depending on the network parameters and the alphabet size. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a lower bound and an upper bound on the gap in the alphabet size between optimal scalar-linear and optimal vector-linear network coding solutions. For a fixed network structure, while varying the number of middle-layer nodes r , the asymptotic behavior of the upper and lower bounds shows that the gap is in \Theta (\log (r)).

Original languageEnglish
Article number9375004
Pages (from-to)5580-5591
Number of pages12
JournalIEEE Transactions on Information Theory
Volume67
Issue number8
DOIs
StatePublished - 1 Aug 2021

Keywords

  • Gap size
  • generalized combination network
  • network coding
  • vector network coding

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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