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.

翻译：由Maddah-Ali和Niesen（MN）最初提出的编码缓存方案针对一个广播网络，该网络包含一台连接至一组用户（每个用户均配备缓存）的服务器。受实际场景启发，Karamchandani等人在文献[16]中提出了一种用于两层分层网络的编码缓存方案，该网络包含一台连接至多个镜像站点的服务器，每个镜像站点连接至一组不同的用户，且镜像站点和用户均配备缓存。低子分组化级别的编码缓存方案对于实际实现至关重要。Yan等人在文献[4]中提出了放置传输数组（PDA）作为设计低子分组化级别编码缓存方案的工具。现有文献中针对单层网络已广泛研究了低子分组化级别的方案。Kong等人在文献[17]中提出了一种称为分层放置传输数组（HPDA）的结构，该结构描述了分层编码缓存系统，并利用两个PDA构造了一类可实现低子分组化级别方案的HPDA。文献[20]中则提出了利用组合t-设计的低子分组化分层方案。除此之外，目前尚无其他工作讨论分层网络中的子分组化问题。本文提出了一类HPDA构造方法，通过先构建一类新型PDA，从而得到低子分组化级别的分层编码缓存方案。与现有方案相比，在系统参数和子分组化级别相同的情况下，所提出的分层方案具有更优的编码延迟。此外，所构建的新型PDA类要么涵盖了现有的若干PDA构造，要么在相同系统参数下实现了更低的传输负载。