Mahesh, AA and Rajan, BS (2022) Minrank of Embedded Index Coding Problems and its Relation to Connectedness of a Bipartite Graph. In: 2022 IEEE Information Theory Workshop, ITW 2022, 1 - 9 November 2022, Mumbai, pp. 702-707.
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Abstract
This paper deals with embedded index coding problem (EICP), introduced by A. Porter and M. Wootters, which is a decentralized communication problem among users with side information. An alternate definition of the parameter minrank of an EICP, which has reduced computational complexity compared to the existing definition, is presented. A graphical representation for an EICP is given using directed bipartite graphs, called bipartite problem graph, and the side information alone is represented using an undirected bipartite graph called the side information bipartite graph. Inspired by the well-studied single unicast index coding problem, graphical structures, similar to cycles and cliques, are identified in the side information bipartite graph of a single unicast embedded index coding problem (SUEICP). Transmission schemes based on these graphical structures, called tree cover scheme and bi-clique cover scheme are also presented. For a class of SUEICPs, scalar linear optimal solution is given using bi-clique cover. A relation between connectedness of the side information bipartite graph and the number of transmissions required in a scalar linear solution of an EICP is established. © 2022 IEEE.
| Item Type: | Conference Paper |
|---|---|
| Publication: | 2022 IEEE Information Theory Workshop, ITW 2022 |
| Publisher: | Institute of Electrical and Electronics Engineers Inc. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Directed graphs; Graph algorithms; Transmissions; Undirected graphs, Bipartite graphs; Coding problems; Covering scheme; Embedded index coding; Graphical representations; Graphical structures; Index coding; Minrank; Side information; Unicast, Graphic methods |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 31 Jan 2023 06:33 |
| Last Modified: | 31 Jan 2023 06:33 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79593 |
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