关于环结构边信息图的索引码
On Index Codes for Interlinked Cycle Structured Side-Information Graphs
摘要：
结合Thapa、Ong和Johnson在\cite{TOJ}中提出的互连环（IC）结构的索引码构造和译码算法（“索引编码的互连循环：Generalizing Cycles and Cliques”，IEEE Trans. Inf. Theory，第63卷，第6期，2017年6月），其在\cite{VaR}中示出（“Optimal Index Codes For A New Class of Interlinked Cycle Structure”，在\textit{IEEE Communication Letters,}中可作为\textit{IEEE Xplore}中的抢先体验文章获得：DOI-10.1109/LCOM.2018.2799202），解码算法并不适用于所有IC结构。在这项工作中，一组必要和充分条件的IC结构的解码算法工作的代码结构中给出的\cite{TOJ}。这些条件被证明是满足的IC结构，没有任何周期组成的只有非内顶点。
英文摘要：
In connection with the index code construction and the decoding algorithm for interlinked cycle (IC) structures proposed by Thapa, Ong and Johnson in \cite{TOJ} ("Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques", IEEE Trans. Inf. Theory, vol. 63, no. 6, Jun. 2017), it is shown in \cite{VaR} ("Optimal Index Codes For A New Class of Interlinked Cycle Structure", in \textit{IEEE Communication Letters,} available as early access article in \textit{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 \cite{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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