Placement Delivery Arrays for Coded Caching with Shared and Private Caches

TL;DR

This paper introduces a new combinatorial structure called SP-PDA for coded caching with shared and private caches, enabling efficient schemes with smaller subpacketization and improved performance.

Contribution

It proposes SP-PDA, a unified framework for coded caching with shared and private caches, and offers a novel construction method using two PDAs, improving subpacketization and performance.

Findings

SP-PDA unifies placement and delivery in a single array.

The construction allows for schemes with smaller subpacketization.

Permutation of PDAs' columns affects performance and can be optimized.

Abstract

We consider a coded caching network consisting of a server with a library of $N$ files connected to $K$ users, where each user is equipped with a dedicated cache of size $M_p$ units. In addition to that, the network consists of $\Lambda\leq K$ helper caches, each with a size $M_h$ units. Each helper cache can serve an arbitrary number of users; however, each user can access only a single helper cache. Also, we assume that the server knows the user-to-helper cache association, defined as the sets of users connected to each helper cache, during the cache placement phase. We propose a solution for the aforementioned coded caching problem by introducing a combinatorial structure called a Shared and Private Placement Delivery Array (SP-PDA). These SP-PDAs describe the helper cache placement, private cache placement, and the server transmissions in a single array. Further, we propose a novel construction of SP-PDAs using two Placement Delivery Arrays (PDAs). Interestingly, we observe that the permutations of the columns of the two chosen PDAs result in SP-PDAs with different performances. Moreover, we characterize the conditions for selecting the best column permutations of the chosen PDAs. Furthermore, the coded caching schemes resulting from SP-PDAs subsume two existing coded caching schemes as special cases. Additionally, SP-PDAs enable the construction of coded caching schemes with much smaller subpacketization numbers -subpacketization number is defined as the number of subfiles to which a file is divided- compared to the existing schemes, without paying much in terms of rate (the size of the transmission in the delivery phase).