  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.
