Centralized Hierarchical Coded Caching Scheme over Two-Layer Networks

TL;DR

This paper introduces a hierarchical placement delivery array (HPDA) to optimize coded caching in two-layer networks, balancing transmission load and subpacketization level, and achieving optimal first-hop load in certain cases.

Contribution

It proposes the HPDA framework and constructs two classes of HPDAs, addressing the optimal first-hop load and subpacketization tradeoff in hierarchical caching systems.

Findings

Achieves optimal R1 in some cases

Reduces subpacketization level with slight load increase

Provides a new structured approach for hierarchical coded caching

Abstract

This paper considers a hierarchical caching system where a server connects with multiple mirror sites, each connecting with a distinct set of users, and both the mirror sites and users are equipped with caching memories. Although there already exist works studying this setup and proposing coded caching scheme to reduce transmission loads, two main problems are remained to address: 1) the optimal communication load under the uncoded placement for the first hop, denoted by $R_1$, is still unknown. 2) the previous schemes are based on Maddah-Ali and Niesen's data placement and delivery, which requires high subpacketization level. How to achieve the well tradeoff between transmission loads and subpacketization level for the hierarchical caching system is unclear. In this paper, we aim to address these two problems. We first propose a new combination structure named hierarchical placement delivery array (HPDA), which characterizes the data placement and delivery for any hierarchical caching system. Then we construct two classes of HPDAs, where the first class leads to a scheme achieving the optimal $R_1$ for some cases, and the second class requires a smaller subpacketization level at the cost of slightly increasing transmission loads.