A Sparse and Low-Rank Optimization Framework for Index Coding via Riemannian Optimization

TL;DR

This paper introduces a novel Riemannian optimization framework for index coding that models the tradeoff between side information and data rate using sparse and low-rank matrices, addressing a fundamental open problem.

Contribution

It proposes a new sparse and low-rank optimization model for index coding and develops a Riemannian optimization approach to solve it effectively.

Findings

Demonstrates the effectiveness of the model through simulations

Reveals the tradeoff between side information and data rate

Provides a new optimization framework for index coding

Abstract

Side information provides a pivotal role for message delivery in many communication scenarios to accommodate increasingly large data sets, e.g., caching networks. Although index coding provides a fundamental modeling framework to exploit the benefits of side information, the index coding problem itself still remains open and only a few instances have been solved. In this paper, we propose a novel sparse and low- rank optimization modeling framework for the index coding problem to characterize the tradeoff between the amount of side information and the achievable data rate. Specifically, sparsity of the model measures the amount of side information, while low- rankness represents the achievable data rate. The resulting sparse and low-rank optimization problem has non-convex sparsity inducing objective and non-convex rank constraint. To address the coupled challenges in objective and constraint, we propose a novel Riemannian optimization framework by exploiting the quotient manifold geometry of fixed-rank matrices, accompanied by a smooth sparsity inducing surrogate. Simulation results demonstrate the appealing sparsity and low-rankness tradeoff in the proposed model, thereby revealing the tradeoff between the amount of side information and the achievable data rate in the index coding problem.