Shared Cache Coded Caching Schemes with known User-to-Cache Association Profile using Placement Delivery Arrays

TL;DR

This paper explores shared cache coded caching schemes using placement delivery arrays (PDAs), demonstrating how column reordering in PDAs can optimize performance while maintaining sub-packetization levels.

Contribution

It introduces a method to reorder PDA columns for improved performance in shared cache networks with known user-to-cache associations.

Findings

Column reordering in PDAs enhances caching scheme performance.

Performance gains are demonstrated for specific PDA classes.

Sub-packetization levels remain unchanged despite reordering.

Abstract

This work considers the coded caching problem with shared caches, where users share the caches, and each user gets access only to one cache. The user-to-cache association is assumed to be known at the server during the placement phase. We focus on the schemes derived using placement delivery arrays (PDAs). The PDAs were originally designed to address the sub-packetization bottleneck of coded caching in a dedicated cache setup. We observe that in the setup of this paper permuting the columns of the PDA results in schemes with different performance for the same problem, but the sub-packetization level remains the same. This is contrary to what was observed for dedicated cache networks. We propose a procedure to identify the ordering of columns that gives the best performance possible for the PDA employed for the given problem. Further, some specific classes of PDAs are chosen and the performance gain achieved by reordering the columns of the PDA is illustrated.