Improved Hotplug Caching Schemes Using PDAs and t-Designs

We consider a coded caching system in which some users are offline at the time of delivery. Such systems are called hotplug coded caching systems \cite{MT2022}, \cite{MT2023}. A placement delivery array (PDA) is a well-known tool for constructing a coded caching scheme for dedicated caches. In this paper, we introduce the concept of PDAs for hotplug coded caching schemes and refer to it as hotplug placement delivery array (HpPDA). We give an algorithm to describe the placement and the delivery phase of a hotplug coded caching scheme using HpPDA. We show that an existing hotplug coded caching scheme given by Y. Ma and D. Tuninetti \cite{MT2022} corresponds to a class of HpPDAs, and then propose a method to further improve the rate of that scheme. Additionally, we construct a class of HpPDA using $t$-designs, which gives a scheme for those memory points that were not covered by existing hotplug caching systems.