  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.
