Optimal-Rate Characterisation for Pliable Index Coding using Absent Receivers

TL;DR

This paper determines the optimal broadcast rate for specific pliable-index-coding problems by developing new bounds that leverage absent receivers, highlighting the importance of receiver sets in rate determination.

Contribution

It introduces novel lower bounds for pliable index coding that incorporate absent receivers, expanding understanding beyond complete-S problems.

Findings

New lower bounds using absent receivers for decoding

Adding any receiver increases broadcast rate in certain classes

Characterization of optimal rates for specific problem classes

Abstract

We characterise the optimal broadcast rate for a few classes of pliable-index-coding problems. This is achieved by devising new lower bounds that utilise the set of absent receivers to construct decoding chains with skipped messages. This work complements existing works by considering problems that are not complete-S, i.e., problems considered in this work do not require that all receivers with a certain side-information cardinality to be either present or absent from the problem. We show that for a certain class, the set of receivers is critical in the sense that adding any receiver strictly increases the broadcast rate.