Design of Coded Caching Schemes with Linear Subpacketizations Based on Injective Arc Coloring of Regular Digraphs

TL;DR

This paper introduces a novel approach to coded caching scheme design using injective arc coloring of regular digraphs, achieving low subpacketization and efficient transmission rates.

Contribution

It proposes a new class of regular digraphs and links their injective arc coloring to PDA design, enabling schemes with linear subpacketization and improved flexibility.

Findings

Derived upper bounds on injective chromatic index of new digraph classes.

Proposed coded caching schemes with linear subpacketization levels.

Generalized existing schemes for more flexible user scenarios.

Abstract

Coded caching is an effective technique to decongest the amount of traffic in the backhaul link. In such a scheme, each file hosted in the server is divided into a number of packets to pursue a low transmission rate based on the delicate design of contents cached into users and broadcast messages. However, the implementation complexity of this scheme increases with the number of packets. It is desirable to design a scheme with a small subpacketization level and a relatively low transmission rate. Recently, placement delivery array (PDA) was proposed to address the subpacketization bottleneck of coded caching. This paper investigates the design PDA from a new perspective, i.e., the injective arc coloring of regular digraphs. It is shown that the injective arc coloring of a regular digraph can yield a PDA with the same number of rows and columns. Based on this, a new class of regular digraphs are defined and the upper bounds on the injective chromatic index of such digraphs are derived. Consequently, some new coded caching schemes with a linear subpacketization level and a small transmission rate are proposed, one of which generalizes the existing scheme for the scenario with a more flexible number of users.