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.

翻译：我们考虑一种编码缓存系统，其中部分用户在交付时刻处于离线状态。此类系统称为热插拔编码缓存系统 \cite{MT2022}, \cite{MT2023}。放置交付数组（PDA）是构建专用缓存编码缓存方案的经典工具。本文引入了用于热插拔编码缓存方案的PDA概念，并将其称为热插拔放置交付数组（HpPDA）。我们提出了一种利用HpPDA描述热插拔编码缓存方案放置与交付阶段的算法。研究表明，Y. Ma和D. Tuninetti \cite{MT2022}提出的现有热插拔编码缓存方案对应一类HpPDA，继而提出改进该方案速率的优化方法。此外，我们利用$t$-设计构造了一类HpPDA，从而为现有热插拔缓存系统未覆盖的记忆点提供了解决方案。