Index coding with side information via penalty method in rank minimisation

Index coding with side information (ICSI) problems can be represented as matrices. These matrices have unique properties with intuitive meaning in its matrix representation. It has been shown by recent studies that minimising the rank of these matrices are equivalent to solving the ICSI problems by finding the minimum index code lengths. This paper investigates the special properties of these matrices associated with the ICSI problems. We will present some theoretical results that will enable us to minimise the rank of these matrices by using a penalty method. The penalty method has been recently shown to have good performance in minimising the rank of positive semidefinite matrices. This paper looks into the implementation of the penalty method to solve ICSI problems. Performance of this implementation will be compared against Alternating Projection (AP) method. AP method has been recently shown to produce promising results in solving ICSI problems by rank minimisation. Key Words: Rank Minimisation, Penalty Method, Proximal Alternating Linearised minimisation, Alternating Projections, Positive SemidefiniteBachelor of Science in Mathematical Science