  Coded caching scheme originally proposed by Maddah-Ali and Niesen (MN)
considered a broadcast network consisting of a single server connected to a set
of users each having a cache memory. Motivated by practical scenarios,
Karamchandani \textit{et al.} in [16] proposed a coded caching scheme for a
two-layer hierarchical network consisting of a single server connected to
multiple mirror sites and each mirror site connected to a distinct set of
users, in which both mirror sites and users having cache memories. Low
subpacketization level coded caching schemes are desirable for practical
implementations. Placement delivery array (PDA) was proposed as a tool to
design coded caching schemes with reduced subpacketization level by Yan
\textit{et al.} in [4]. Schemes with reduced subpacketization levels are
studied extensively in the literature for single-layer networks. Kong
\textit{et al.} in [17] proposed a structure called hierarchical placement
delivery arrays (HPDA), which characterizes a hierarchical coded caching system
and also proposed a class of HPDAs that gives low subpacketization level
schemes by using two PDAs. Low subpacketization level hierarchical schemes
using combinatorial $t$-designs is proposed in [20]. Apart from that there is
no other existing work that discusses the subpacketization problem in a
hierarchical network. This paper proposes a class of HPDA construction that
gives low subpacketization level hierarchical coded caching schemes, by first
constructing a new class of PDAs. Compared with the existing schemes, in cases
where the system parameters and subpacketization level are the same, the
proposed hierarchical scheme has a better coding delay. Further, the new class
of PDAs constructed either subsumes several known PDA constructions or achieves
better transmission load for the same system parameters.
