On Pliable Index Coding

TL;DR

This paper introduces and analyzes the Pliable Index Coding Problem (PICOD), focusing on cases with consecutive side information, and proposes index coding solutions for specific extreme and constrained scenarios.

Contribution

It formulates the PICOD with consecutive side information and provides novel index coding solutions for extreme and c-constrained cases.

Findings

Provided index codes for clients with exactly one desired message.

Maximized total messages decoded by effective clients.

Extended solutions to c-constrained PICOD with consecutive side information.

Abstract

A new variant of index coding problem termed as Pliable Index Coding Problem (PICOD) is formulated in [S. Brahma, C. Fragouli, "Pliable index coding", IEEE Transactions on Information Theory, vol. 61, no. 11, pp. 6192-6203, 2015]. In PICOD, we consider a server holding a set of messages and there is a set of clients having a subset of messages with them. Each client is satisfied if it receives any of the message which it doesn't have. We discuss about a class of PICOD where the side information is consecutive. We provide index codes for two extreme cases - for the class where each client gets exactly one desired message and for a class where total number of messages decoded by the effective clients is maximized. Another variant of index coding problem is - c-Constrained Pliable Index Coding Problem [Linqi Song, Christina Fragouli and Tianchu Zhao, "A Pliable Index Coding Approach to Data Shuffling," arXiv:1701.05540v3 [cs.IT] 3 May 2018]. It is basically PICOD with a c-constraint, i.e, each message is decoded by atmost c clients demanding that message. We provide index codes for some classes of this variant with consecutive side information.