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

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 number of users connected to each cache 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 performances 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 from the PDA employed in the given problem. Further, the performance gain achieved by reordering the columns of the PDA is illustrated using certain classes of PDAs.