On the Conjectures on Optimality of Index Codes from Interlinked Cycle Cover Scheme

The interlinked cycle (IC) structure, that generalizes cycles and cliques was defined by Thapa, Ong and Johnson. Interlinked-cycle-cover (ICC) scheme that leverages IC structures in digraphs to construct scalar linear index codes was proposed. Thapa $et$, al. conjectured that for any IC structure, the ICC scheme is optimal. It was also conjectured that for any digraph, the ICC scheme performs at least as well as the partial-clique-cover scheme. In this paper, we disprove both the conjectures. We also show that for a specific class of symmetric index coding problems, the performance of ICC scheme is equal to that of the partial-clique-cover scheme.

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