Coded Caching with Shared Caches: Fundamental Limits with Uncoded Prefetching

TL;DR

This paper establishes the fundamental limits of coded caching with shared helper caches under uncoded prefetching, proving the optimality of a simple XOR-based scheme across various user-cache associations.

Contribution

It derives the exact optimal worst-case delivery time for shared caches with uncoded placement, using a new information-theoretic converse based on index coding.

Findings

Optimal worst-case delivery time derived for shared caches

XOR-shrinking scheme proven to be optimal

Results extend to multiple file requests

Abstract

The work identifies the fundamental limits of coded caching when the K receiving users share {\Lambda}$\leq$ K helper-caches, each assisting an arbitrary number of different users. The main result is the derivation of the exact optimal worst-case delivery time - under the assumption of uncoded cache placement - for any user-to-cache association profile, where each such profile describes how many users are helped by each cache. This is achieved with a new information-theoretic converse that is based on index coding and which proves that a simple XOR-shrinking-and-removal coded-caching scheme is optimal irrespective of the user-to-cache association profile. All the results also apply directly to the coded caching problem with multiple file requests.