Constructing Index Codes with Coded Demands and Side Information through Matrix Completion

Abstract

We consider the problem of constructing index codes that maximize network throughput. In index coding, multiple users, with some side information, demand certain subsets of data from a server. The goal of index code is to minimize the required transmission rate at the server while ensuring that the users can recover the demanded data using the index coded broadcast message from the server. We consider a generalized version of the index coding problem, where both the side information and user-demanded data can be coded. The problem of index code construction for a given set of side information and users' demands, can be modeled as a matrix completion problem. Traditional matrix completion algorithms do not take advantage of the inherent structure in the index codes to construct efficient index codes. In this paper, using generalized proximal gradient and low-rank matrix factorization approaches, we develop matrix completion algorithms that take into account the structure in the index coding problem to construct efficient index codes. Through numerical simulations, we show that the proposed matrix completion methods construct efficient index codes compared to the traditional methods known in the literature so far.