Improved Lower Bounds for Coded Caching

TL;DR

This paper introduces a new combinatorial approach to derive tighter lower bounds for coded caching rates, narrowing the gap between achievable and theoretical limits in content delivery networks.

Contribution

It presents a novel labeling algorithm for the leaves of a directed tree to improve lower bounds on coded caching rates, achieving a maximum fourfold gap with known achievable rates.

Findings

Derived tighter lower bounds on coded caching rates.

Proposed a leaf-labeling algorithm for directed trees.

Quantified improvements analytically for general parameters.

Abstract

Content delivery networks often employ caching to reduce transmission rates from the central server to the end users. Recently, the technique of coded caching was introduced whereby coding in the caches and coded transmission signals from the central server are considered. Prior results in this area demonstrate that carefully designing the placement of content in the caches and designing appropriate coded delivery signals from the server allow for a system where the delivery rates can be significantly smaller than conventional schemes. However, matching upper and lower bounds on the transmission rate have not yet been obtained. In this work, we derive tighter lower bounds on the coded caching rate than were known previously. We demonstrate that this problem can equivalently be posed as a combinatorial problem of optimally labeling the leaves of a directed tree. Our proposed labeling algorithm allows for significantly improved lower bounds on the coded caching rate. Furthermore, we study certain structural properties of our algorithm that allow us to analytically quantify improvements on the rate lower bound for general values of the problem parameters. This allows us to obtain a multiplicative gap of at most four between the achievable rate and our lower bound.