A New Class of Index Coding Instances Where Linear Coding is Optimal
Abstract
We study indexcoding problems (one sender broadcasting messages to multiple receivers) where each message is requested by one receiver, and each receiver may know some messages a priori. This type of indexcoding problems can be fully described by directed graphs. The aim is to find the minimum codelength that the sender needs to transmit in order to simultaneously satisfy all receivers' requests. For any directed graph, we show that if a maximum acyclic induced subgraph (MAIS) is obtained by removing two or fewer vertices from the graph, then the minimum codelength (i.e., the solution to the indexcoding problem) equals the number of vertices in the MAIS, and linear codes are optimal for this indexcoding problem. Our result increases the set of indexcoding problems for which linear index codes are proven to be optimal.
 Publication:

arXiv eprints
 Pub Date:
 September 2013
 DOI:
 10.48550/arXiv.1309.4166
 arXiv:
 arXiv:1309.4166
 Bibcode:
 2013arXiv1309.4166O
 Keywords:

 Computer Science  Information Theory
 EPrint:
 accepted and to be presented at the 2014 International Symposium on Network Coding (NetCod)