Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques

@article{Thapa2017InterlinkedCF,
  title={Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques},
  author={Chandra Thapa and Lawrence Ong and Sarah J. Johnson},
  journal={IEEE Transactions on Information Theory},
  year={2017},
  volume={63},
  pages={3692-3711}
}
We consider a graphical approach to index coding. As cycles have been shown to provide coding gain, cycles and cliques (a specific type of overlapping cycles) have been exploited in an existing literature. In this paper, we define a more general form of overlapping cycles, called the interlinked-cycle (<inline-formula> <tex-math notation="LaTeX">$ \mathsf {IC} $ </tex-math></inline-formula>) structure, that generalizes cycles and cliques. We propose a scheme, called the interlinked-cycle-cover… 
On Index Codes for Interlinked Cycle Structured Side-Information Graphs
TLDR
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}.
Optimal Index Codes for Some Interlinked Cycle Structures with Outer Cycles
TLDR
For IC structures with interlocked outer cycles it is shown that the optimal length (also known as the minrank of the index coding problem) depends on the maximum number of disjoint outer cycles.
Index Codes for Interlinked Cycle Structures with Outer Cycles
  • K. BharadwajB. S. Rajan
  • Computer Science
    2018 International Symposium on Information Theory and Its Applications (ISITA)
  • 2018
TLDR
This paper gives a set of necessary and sufficient conditions for the code construction and the decoding algorithm of Thapa, Ong and Johnson to be valid for Interlinked Cycle structures with outer cycles.
Construction of Index Codes for Interlinked Cycle Structures with Outer Cycles
TLDR
This paper presents an algorithm for index code construction and decoding algorithm for interlinked cycle structures with outer cycles, which generalize cycles and cliques.
On the Structure of Interlinked Cycle Structures with Interlocked Outer Cycles
TLDR
Certain structural properties of IC structures with interlocked outer cycles are discussed and a simple algorithm is provided to find the maximum number of disjoint outer cycles.
A Generalisation of Interlinked Cycle Structures and Their Index Coding Capacity
TLDR
The index coding capacity of OIC structures is proved by giving an index code with length equal to the order of maximum acyclic induced subgraph (MAIS) of OI structures.
Optimal Index Codes for a New Class of Interlinked Cycle Structure
TLDR
A class of infinitely many digraphs, where the proposed scalar linear codes based on ICC scheme are optimal were characterized, is provided by providing optimal length index codes for IC structures with one cycle among non-inner vertex set.
On the Conjectures on Optimality of Index Codes from Interlinked Cycle Cover Scheme
TLDR
It is shown that for a specific class of symmetric index coding problems, the performance of ICC scheme is equal to that of the partial-clique-cover scheme.
Index Coding: Rank-Invariant Extensions
TLDR
This work presents a straightforward m-order extension of an IC problem and constructions of such extensions based on involutory permutation matrices, and focuses on 2-order rank-invariant extensions of the problem.
Corrections to "Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques"
TLDR
This work adds one extra condition for the definition of an $\mathsf {IC}$ structure on page 3696 and provides a correction to [1] in response to an error reported by Vaddi and Rajan.
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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}.
Optimal Index Codes for a New Class of Interlinked Cycle Structure
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A class of infinitely many digraphs, where the proposed scalar linear codes based on ICC scheme are optimal were characterized, is provided by providing optimal length index codes for IC structures with one cycle among non-inner vertex set.
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This work adds one extra condition for the definition of an $\mathsf {IC}$ structure on page 3696 and provides a correction to [1] in response to an error reported by Vaddi and Rajan.
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