Local Graph Coloring and Index Coding
Information Theory
2013-02-12 v2 Discrete Mathematics
math.IT
Abstract
We present a novel upper bound for the optimal index coding rate. Our bound uses a graph theoretic quantity called the local chromatic number. We show how a good local coloring can be used to create a good index code. The local coloring is used as an alignment guide to assign index coding vectors from a general position MDS code. We further show that a natural LP relaxation yields an even stronger index code. Our bounds provably outperform the state of the art on index coding but at most by a constant factor.
Keywords
Cite
@article{arxiv.1301.5359,
title = {Local Graph Coloring and Index Coding},
author = {Karthikeyan Shanmugam and Alexandros G. Dimakis and Michael Langberg},
journal= {arXiv preprint arXiv:1301.5359},
year = {2013}
}
Comments
14 Pages, 3 Figures; A conference version submitted to ISIT 2013; typos corrected