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This paper considers a hierarchical caching system where a server connectswith multiple mirror sites, each connecting with a distinct set of users, andboth the mirror sites and users are equipped with caching memories. Althoughthere already exist works studying this setup and proposing coded cachingscheme to reduce transmission loads, two main problems are remained to address:1) the optimal communication load under the uncoded placement for the firsthop, denoted by $R_1$, is still unknown. 2) the previous schemes are based onMaddah-Ali and Niesen's data placement and delivery, which requires highsubpacketization level. How to achieve the well tradeoff between transmissionloads and subpacketization level for the hierarchical caching system isunclear. In this paper, we aim to address these two problems. We first proposea new combination structure named hierarchical placement delivery array (HPDA),which characterizes the data placement and delivery for any hierarchicalcaching system. Then we construct two classes of HPDAs, where the first classleads to a scheme achieving the optimal $R_1$ for some cases, and the secondclass requires a smaller subpacketization level at the cost of slightlyincreasing transmission loads.

Centralized Hierarchical Coded Caching Scheme over Two-Layer Networks