On the Gap between Scalar and Vector Solutions of Generalized Combination Networks
Information Theory
2020-05-13 v2 Social and Information Networks
Combinatorics
math.IT
Probability
Abstract
We study scalar-linear and vector-linear solutions to 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. These bounds improve and extend the parameter range of known bounds. Using these new bounds we present a general lower bound on the gap in the alphabet size between scalar-linear and vector-linear solutions.
Keywords
Cite
@article{arxiv.2001.04150,
title = {On the Gap between Scalar and Vector Solutions of Generalized Combination Networks},
author = {Hedongliang Liu and Hengjia Wei and Sven Puchinger and Antonia Wachter-Zeh and Moshe Schwartz},
journal= {arXiv preprint arXiv:2001.04150},
year = {2020}
}
Comments
6 pages, 1 figures, accepted by ISIT 2020, revised according to the reviews