On Index Codes for Interlinked Cycle Structured Side-Information Graphs

In connection with the index code construction and the decoding algorithm for interlinked cycle (IC) structures proposed by Thapa, Ong and Johnson in [1] (”Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques”, IEEE Trans. Inf. Theory, vol. 63, no. 6, Jun. 2017), it is shown in [6] (”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 [1]. These conditions are shown to be satisfied for the IC structures without any cycles consisting of only non-inner vertices. 1