Effect of Number of Users in Multi-level Coded Caching

TL;DR

This paper investigates how the number of users per cache affects the optimal design of multi-level coded caching systems, revealing different strategies for single-user and multi-user scenarios.

Contribution

It introduces a dichotomy in order-optimal caching strategies for single-user and multi-user setups within multi-level popularity models, supported by new information-theoretic bounds.

Findings

Sharing memory among levels is optimal in multi-user setups.

Clustering levels and allocating all memory to them is optimal in single-user setups.

Develops new lower bounds for the caching problem.

Abstract

It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. This has also been extended to the case when content has non-uniform popularity through several models. In this paper we focus on a multi-level popularity model, where content is divided into levels based on popularity. We consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup). When the capacity approximation is universal (independent of number of popularity levels as well as number of users, files and caches), we demonstrate a dichotomy in the order-optimal strategies for these two extreme cases. In the multi-user case, sharing memory among the levels is order-optimal, whereas for the single-user case clustering popularity levels and allocating all the memory to them is the order-optimal scheme. In proving these results, we develop new information-theoretic lower bounds for the problem.