Optimal Index Codes for a New Class of Interlinked Cycle Structure

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. A class of infinitely many digraphs, where the proposed scalar linear codes based on ICC scheme are optimal were characterized by Thapa et. al. In this paper, we provide an addition to this class by providing optimal length index codes for IC structures with one cycle among non-inner vertex set.

[1]  Ziv Bar-Yossef,et al.  Index Coding With Side Information , 2011, IEEE Trans. Inf. Theory.

[2]  Yitzhak Birk,et al.  Informed-source coding-on-demand (ISCOD) over broadcast channels , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[3]  Lawrence Ong,et al.  Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques , 2016, IEEE Transactions on Information Theory.

[4]  Robert D. Kleinberg,et al.  Broadcasting With Side Information: Bounding and Approximating the Broadcast Rate , 2013, IEEE Transactions on Information Theory.

[5]  Lawrence Ong,et al.  The Single-Uniprior Index-Coding Problem: The Single-Sender Case and the Multi-Sender Extension , 2016, IEEE Transactions on Information Theory.