2017/01/24 by V. Lalitha, Prasad Krishnan, Lalitha, V. +1
Computer Science · Engineering · #Advanced MIMO Systems Optimization #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.1701.06814
openalex publication_date 2017/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Linear index coding can be formulated as an interference alignment problem, in which precoding vectors of the minimum possible length are to be assigned to the messages in such a way that the precoding vector of a demand (at some receiver) is independent of the space of the interference (non side-information) precoding vectors. An index code has rate (1)/(l) if the assigned vectors are of length l. In this paper, we introduce the notion of strictly rate (1)/(L) message subsets which must necessarily be allocated precoding vectors from a strictly L-dimensional space (L=1,2,3) in any rate (1)/(3) code. We develop a general necessary condition for rate (1)/(3) feasibility using intersections of strictly rate (1)/(L) message subsets. We apply the necessary condition to show that the presence of certain interference configurations makes the index coding problem rate (1)/(3) infeasible. We also obtain a class of index coding problems, containing certain interference configurations, which are rate (1)/(3) feasible based on the idea of contractions of an index coding problem. Our necessary conditions for rate (1)/(3) feasibility and the class of rate (1)/(3) feasible problems obtained subsume all such known results for rate (1)/(3) index coding.