A class of index coding problems with rate 1/3

An index coding problem with n messages has symmetric rate R if all n messages can be conveyed at rate R. In a recent work, a class of index coding problems for which symmetric rate 1/3 is achievable was characterised using special properties of the side-information available at the receivers. In this paper, we show a larger class of index coding problems (which includes the previous class of problems) for which symmetric rate 1/3 is achievable. In the process, we also obtain a stricter necessary condition for rate 1/3 feasibility than what is known in literature.