Blind Updates in Coded Caching

TL;DR

This paper introduces a new method for efficiently updating cached files in a centralized coded caching system when files are replaced with correlated new versions, minimizing broadcast communication.

Contribution

It proposes a novel coded transmission strategy for blind cache updates and derives bounds on the minimal communication cost, improving efficiency in correlated file replacement scenarios.

Findings

New coded update scheme reduces broadcast cost for sparse updates.

MDS-based scheme is order-optimal for dense updates.

Derived converse bounds for linear strategies.

Abstract

We consider the centralized coded caching system where a library of files is available at the server and their subfiles are cached at the clients as prescribed by a placement delivery array (PDA). We are interested in the problem where a specific file in the library is replaced with a new file at the server, the contents of which are correlated with the file being replaced, and this change needs to be communicated to the caches. Upon replacement, the server has access only to the updated file and is unaware of its differences with the original, while each cache has access to specific subfiles of the original file as dictated by the PDA. We model the correlation between the two files by assuming that they differ in at the most $\epsilon$ subfiles, and aim to reduce the number of bits broadcast by the server to update the caches. We design a new elegant coded transmission strategy for the server to update the caches blindly, and also identify a simple scheme that is based on MDS codes. We then derive converse bounds on the minimum communication cost $\ell^*$ among all linear strategies. For two well-known families of PDAs -- Maddah-Ali & Niesen's caching scheme and a PDA by Tang & Ramamoorthy and Yan et al. -- our new scheme has cost $\ell^*(1 + o(1))$ when the updates are sufficiently sparse, while the scheme using MDS codes has order-optimal cost when the updates are dense.