Index Codes for Interlinked Cycle Structures with Outer Cycles
Karanam Vikas Bharadwaj, Balaji Sundar Rajan · 2018
For side-information graphs called Interlinked Cycle (IC) structures, which generalize cycles and cliques, Thapa, Ong and Johnson ("Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", IEEE Trans. Inf. Theory, vol. 63, no. 6, Jun. 2017 and "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", in arxiv (arxiv:1603.00092v2 [cs.IT] 25 Feb 2018)) have given an index code construction and a decoding algorithm, for the case where the IC structure does not have any cycles consisting only of non-inner vertices (called outer cycles). In this paper, for IC structures with outer cycles, we give a set of necessary and sufficient conditions for the code construction and the decoding algorithm of Thapa, Ong and Johnson to be valid.