On Index Codes for Interlinked Cycle Structured Side-Information Graphs
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In connection with the index code construction and the decoding algorithm for interlinked cycle (IC) structures proposed by Thapa, Ong and Johnson in TOJ ("Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", IEEE Trans. Inf. Theory, vol. 63, no. 6, Jun. 2017), it is shown in VaR ("Optimal Index Codes For A New Class of Interlinked Cycle Structure", in IEEE Communication Letters, available as early access article in IEEE Xplore: DOI-10.1109/LCOMM.2018.2799202) that the decoding algorithm does not work for all IC structures. In this work, a set of necessary and sufficient conditions on the IC structures is presented for the decoding algorithm to work for the code construction given in TOJ. These conditions are shown to be satisfied for the IC structures without any cycles consisting of only non-inner vertices.
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