Improved Hotplug Caching Schemes Using PDAs and t-Designs
Charul Rajput, B. Sundar Rajan
TL;DR
This work addresses hotplug coded caching, where only a subset of users is active at delivery, by extending the placement delivery array (PDA) framework to HpPDA. It develops a systematic algorithm to realize placement and delivery from HpPDAs and demonstrates how existing MT2022 schemes map to MAN HpPDAs, enabling rate improvements. The authors then construct HpPDAs from $t$-designs, providing multi-point rate-memory tradeoffs and showing expanded optimality results, including exact cut-set bound attainment for certain three-user cases. Numerical results illustrate improved rates and lower subpacketization relative to MT2022, highlighting practical gains for hotplug scenarios and guiding future explorations of additional HpPDA classes and designs.
Abstract
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. 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 a 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 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 prove that the cut-set bound is achieved in some higher memory range for a hotplug coded caching system with three active users.