# A Generalisation of Interlinked Cycle Structures and Their Index Coding Capacity

## TL;DR

This paper extends the concept of interlinked cycle structures in side-information graphs to overlapping interlinked cycle (OIC) structures, providing a capacity proof and a construction for scalar linear index codes.

## Contribution

It introduces OIC structures, generalizing IC structures, and proves their capacity by constructing optimal index codes matching the MAIS of the graph.

## Key findings

- Capacity of OIC structures is equal to the size of the maximum acyclic induced subgraph.
- Provides a scalar linear index coding scheme for OIC structures.
- Generalizes previous IC-based index coding schemes.

## Abstract

Cycles and Cliques in a side-information graph reduce the number of transmissions required in an index coding problem. Thapa, Ong and Johnson defined a more general form of overlapping cycles, called the interlinked-cycle (IC) structure, that generalizes cycles and cliques. They proposed a scheme, that leverages IC structures in digraphs to construct scalar linear index codes. In this paper, we extend the notion of interlinked cycle structure to define more generalised graph structures called overlapping interlinked cycle (OIC) structures. We prove the capacity of OIC structures by giving an index code with length equal to the order of maximum acyclic induced subgraph (MAIS) of OIC structures.