Coded Caching with Shared Caches from Generalized Placement Delivery Arrays

TL;DR

This paper introduces a method to adapt placement delivery arrays (PDAs) for shared cache coded caching, significantly reducing sub-packetization requirements while maintaining optimality.

Contribution

It presents a procedure to convert existing PDA structures into efficient coded caching schemes for shared caches, addressing sub-packetization challenges.

Findings

New low sub-packetization schemes derived from existing PDAs

Unified framework for shared cache coded caching schemes

Recovery of optimal schemes using Maddah-Ali Niesen PDA

Abstract

We consider the coded caching problem with shared caches where several users share a cache, but each user has access to only a single cache. For this network, the fundamental limits of coded caching are known for centralized and decentralized settings under uncoded placement. In the centralized case, to achieve the gains offered by coded caching, one requires a sub-packetization which increases exponentially with the number of caches. The dedicated cache networks had a similar issue, and placement delivery arrays (PDAs) were introduced as a solution to it. Using the PDA framework, we propose a procedure to obtain new coded caching schemes for shared caches with lower sub-packetization requirements. The advantage of this procedure is that we can transform all the existing PDA structures into coded caching schemes for shared caches, thus resulting in low sub-packetization schemes. We also show that the optimal scheme given by Parrinello, Unsal and Elia (Fundamental Limits of Coded Caching with Multiple Antennas, Shared Caches and Uncoded Prefetching) can be recovered using a Maddah-Ali Niesen PDA.