A New Converse Bound for Coded Caching

TL;DR

This paper develops a new information-theoretic lower bound for coded caching, significantly tightening the known bounds and providing insights into optimal caching strategies for different request distributions.

Contribution

It introduces a novel lower bound for the caching problem, improving the analytical gap to optimality and analyzing optimal strategies for multiple file requests.

Findings

Lower bound reduces the gap to optimal from 12 to 4.7.

The bound tightens the gap for uniform request distribution.

Caching the most requested files is optimal for single-user multiple requests.

Abstract

An information-theoretic lower bound is developed for the caching system studied by Maddah-Ali and Niesen. By comparing the proposed lower bound with the decentralized coded caching scheme of Maddah-Ali and Niesen, the optimal memory--rate tradeoff is characterized to within a multiplicative gap of $4.7$ for the worst case, improving the previous analytical gap of $12$. Furthermore, for the case when users' requests follow the uniform distribution, the multiplicative gap is tightened to $4.7$, improving the previous analytical gap of $72$. As an independent result of interest, for the single-user average case in which the user requests multiple files, it is proved that caching the most requested files is optimal.