Multi-Library Coded Caching

TL;DR

This paper investigates coded caching across multiple libraries, establishing optimal strategies for equal-sized libraries and proposing bounds for the general case with arbitrary library sizes.

Contribution

It proves that memory-sharing is optimal for equal-sized libraries and introduces bounds for the more complex scenario with varying library sizes.

Findings

Memory-sharing is optimal when all libraries have the same number of files.

The optimal cache division is proportional to library sizes.

Outer and inner bounds are proposed for arbitrary library sizes.

Abstract

We study the problem of coded caching when the server has access to several libraries and each user makes independent requests from every library. The single-library scenario has been well studied and it has been proved that coded caching can significantly improve the delivery rate compared to uncoded caching. In this work we show that when all the libraries have the same number of files, memory-sharing is optimal and the delivery rate cannot be improved via coding across files from different libraries. In this setting, the optimal memory-sharing strategy is one that divides the cache of each user proportional to the size of the files in different libraries. As for the general case, when the number of files in different libraries are arbitrary, we propose an inner-bound based on memory-sharing and an outer-bound based on concatenation of files from different libraries.