Improved Lower Bounds for Pliable Index Coding using Absent Receivers

TL;DR

This paper advances the understanding of pliable index coding by developing new techniques to establish tighter lower bounds and determining optimal broadcast rates for cases with up to four absent receivers.

Contribution

It introduces novel methods to improve lower bounds and solves for the optimal broadcast rates in new problem classes involving absent receivers.

Findings

New techniques yield tighter lower bounds.

Optimal broadcast rates found for problems with up to four absent receivers.

Enhanced understanding of pliable index coding bounds.

Abstract

This paper studies pliable index coding, in which a sender broadcasts information to multiple receivers through a shared broadcast medium, and the receivers each have some message a priori and want any message they do not have. An approach, based on receivers that are absent from the problem, was previously proposed to find lower bounds on the optimal broadcast rate. In this paper, we introduce new techniques to obtained better lower bounds, and derive the optimal broadcast rates for new classes of the problems, including all problems with up to four absent receivers.