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 a system is known as a hotplug coded caching system. A placement delivery array (PDA) is a well-known tool for constructing coded caching schemes for caching systems with dedicated caches. In this paper, we introduce the concept of PDAs for hotplug coded caching schemes and refer to it as hotplug placement delivery arrays (HpPDAs). We provide an algorithm to describe the placement and the delivery phase of a hotplug coded caching scheme using an HpPDA. We show that an existing hotplug coded caching scheme given by Y. Ma and D. Tuninetti in 2022 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 HpPDAs using $ t $-designs, which corresponds to a scheme for hotplug coded caching systems. We further improve the rate of this scheme and compare it with existing schemes for several examples. We also prove that it achieves the cut-set bound in some high memory range.