Information Theoretic Caching: The Multi-User Case

TL;DR

This paper develops an information theoretic framework for cache-aided networks with multiple users, providing bounds on the tradeoff between cache size and update rate, and improves existing bounds for content delivery scenarios.

Contribution

It introduces a general information theoretic model for cache networks, derives new bounds, and extends existing strategies to better characterize the rate-cache tradeoff.

Findings

Characterized the rate vs. cache size tradeoff within a factor of 4 for uniform requests.

Established new inner and outer bounds for content delivery networks.

Improved the multiplicative gap from 72 to 4.7 for average case scenarios.

Abstract

In this paper, we consider a cache aided network in which each user is assumed to have individual caches, while upon users' requests, an update message is sent though a common link to all users. First, we formulate a general information theoretic setting that represents the database as a discrete memoryless source, and the users' requests as side information that is available everywhere except at the cache encoder. The decoders' objective is to recover a function of the source and the side information. By viewing cache aided networks in terms of a general distributed source coding problem and through information theoretic arguments, we present inner and outer bounds on the fundamental tradeoff of cache memory size and update rate. Then, we specialize our general inner and outer bounds to a specific model of content delivery networks: File selection networks, in which the database is a collection of independent equal-size files and each user requests one of the files independently. For file selection networks, we provide an outer bound and two inner bounds (for centralized and decentralized caching strategies). For the case when the user request information is uniformly distributed, we characterize the rate vs. cache size tradeoff to within a multiplicative gap of 4. By further extending our arguments to the framework of Maddah-Ali and Niesen, we also establish a new outer bound and two new inner bounds in which it is shown to recover the centralized and decentralized strategies, previously established by Maddah-Ali and Niesen. Finally, in terms of rate vs. cache size tradeoff, we improve the previous multiplicative gap of 72 to 4.7 for the average case with uniform requests.