Combinatorial Multi-Access Coded Caching with Private Caches

TL;DR

This paper studies a novel multi-access coded caching system with private caches, proposing an achievable scheme, deriving bounds, and analyzing its optimality, especially when users access multiple caches and have private storage.

Contribution

It introduces a new combinatorial multi-access coded caching model with private caches, providing achievable schemes, bounds, and analysis of optimality under uncoded placement.

Findings

Proposed an achievable caching scheme for the new model.

Derived lower and upper bounds on the worst-case rate.

The scheme approaches the lower bound when user memory access is large.

Abstract

We consider a variant of the coded caching problem where users connect to two types of caches, called private and access caches. The problem setting consists of a server with a library of files and a set of access caches. Each user, equipped with a private cache, connects to a distinct $r-$subset of the access caches. The server populates both types of caches with files in uncoded format. For this setting, we provide an achievable scheme and derive a lower bound on the number of transmissions for this scheme. We also present a lower and upper bound for the optimal worst-case rate under uncoded placement for this setting using the rates of the Maddah-Ali--Niesen scheme for dedicated and combinatorial multi-access coded caching settings, respectively. Further, we derive a lower bound on the optimal worst-case rate for any general placement policy using cut-set arguments. We also provide numerical plots comparing the rate of the proposed achievability scheme with the above bounds, from which it can be observed that the proposed scheme approaches the lower bound when the amount of memory accessed by a user is large. Finally, we discuss the optimality w.r.t worst-case rate when the system has four access caches.