Index Coding and Network Coding via Rank Minimization

TL;DR

This paper explores rank minimization heuristics like alternating projections for constructing efficient linear index codes, achieving up to 13% savings over traditional graph coloring methods, and extends these techniques to network coding.

Contribution

It introduces rank minimization heuristics for index coding, demonstrating their effectiveness and extending their application to non-multicast network coding scenarios.

Findings

Alternating projections yields the best index coding results.

Up to 13% reduction in communication cost compared to graph coloring.

Methods can be applied to construct linear network codes for non-multicast networks.

Abstract

Index codes reduce the number of bits broadcast by a wireless transmitter to a number of receivers with different demands and with side information. It is known that the problem of finding optimal linear index codes is NP-hard. We investigate the performance of different heuristics based on rank minimization and matrix completion methods, such as alternating projections and alternating minimization, for constructing linear index codes over the reals. As a summary of our results, the alternating projections method gives the best results in terms of minimizing the number of broadcast bits and convergence rate and leads to up to 13% savings in average communication cost compared to graph coloring algorithms studied in the literature. Moreover, we describe how the proposed methods can be used to construct linear network codes for non-multicast networks. Our computer code is available online.