Abstract
Linear index coding can be formulated as an inter-ference alignment problem, in which precoding vectors of theminimum possible length are to be assigned to the messagesin such a way that the precoding vector of a demand (at somereceiver) is independent of the space of the interference (non side-information) precoding vectors. An index code has rate1lif theassigned vectors are of lengthl. In this paper, we introduce thenotion of strictly rate1Lmessage subsets which must necessarilybe allocated precoding vectors from a strictlyL-dimensionalspace (L=1,2,3) in any rate13code. We develop a generalnecessary condition for rate13feasibility using intersections ofstrictly rate1Lmessage subsets. We apply the necessary conditionto show that the presence of certain interference configurationsmakes the index coding problem rate13infeasible. We alsoobtain a class of index coding problems, containing certaininterference configurations, which are rate13feasible based on theidea ofcontractionsof an index coding problem. Our necessaryconditions for rate13feasibility and the class of rate13feasibleproblems obtained subsume all such known results for rate13index coding