A New Hotplug Coded Caching Scheme Using PDAs
Mallikharjuna Chinnapadamala, Charul Rajput, B. Sundar Rajan
TL;DR
The paper addresses hotplug coded caching where only $K'$ users are active during delivery and their identities are unknown during placement. It proposes a new scheme that leverages existing HpPDAs by partitioning each file into $F'-Z'+Z$ subfiles, applying an $[F,F'-Z'+Z]$ MDS encoding, and using HpPDA-based placement and transmissions to serve the active users. For a given HpPDA, the scheme achieves the memory-rate point $(M/N,R)=(Z/(F'-Z'+Z), S/(F'-Z'+Z))$, with explicit MAN and $t$-design instantiations analyzed. Numerical comparisons show improvements over the baseline MaT and Improved $t$-scheme in several memory ranges, albeit at the cost of higher subpacketization, signaling a new tradeoff in hotplug coded caching designs.
Abstract
In the original coded caching model introduced by Maddah-Ali and Niesen in 2014, the server starts broadcasting only after it receives demands from all the users. So, all the users must be active during the delivery phase. In this work, we consider a coded caching model called hotplug coded caching in which some of the users are offline during the delivery phase. This model was first introduced by Ma and Tuninetti (``On Coded Caching Systems with Offline Users," 2022 IEEE International Symposium on Information Theory). The concept of Hotplug Placement Delivery Arrays (HpPDAs) for the hotplug coded caching systems was introduced in (``Improved Hotplug Caching Schemes Using PDAs and $t$-Designs," \emph{arXiv:2311.02856}, 2024), in which the authors have constructed HpPDAs from $t$-designs. This work provides a new hotplug coded caching scheme from the existing HpPDAs. The performance comparison of the proposed scheme with the existing schemes is presented. When applied for HpPDAs from $t$-designs, our scheme outperforms the baseline scheme by Ma and Tuninetti, and the Improved $t$-scheme by Rajput and Rajan in some memory regimes.