Combinatorial Analysis of Coded Caching Schemes

TL;DR

This paper analyzes the trade-offs in coded caching schemes, optimizing their design under packet number constraints and presenting new constructions for optimal schemes within these limits.

Contribution

It introduces a new optimization framework for coded caching schemes considering packet limitations and provides constructions for infinite classes of optimal solutions.

Findings

Optimized coded caching schemes under packet constraints.

Constructed infinite classes of optimal schemes.

Balanced trade-off between data splitting and information rate.

Abstract

Coded caching schemes are used to reduce computer network traffics in peak time. To determine the efficiency of the schemes, \cite{MN} defined the information rate of the schemes and gave a construction of optimal coded caching schemes. However, their construction needs to split the data into a large number of packets which may cause constraints in real applications. Many researchers then constructed new coded caching schemes to reduce the number of packets but that increased the information rate. We define an optimization of coded caching schemes under the limitation of the number of packets which may be used to verify the efficiency of these schemes. We also give some constructions for several infinite classes of optimal coded caching schemes under the new definition.