Hierarchical Coded Caching With Low Subpacketization and Coding Delay Using Combinatorial t-Designs

Multi-layer cache structures are commonly used in various IoT environments due to their distributed architecture. This paper considers coded caching for a two-layer hierarchical network consisting of a single server connected to multiple cache-aided mirror sites, and each mirror site connected to a distinct set of cache-aided users. The placement delivery array (PDA) and the hierarchical placement delivery array (HPDA) were proposed as tools for designing coded caching schemes with reduced subpacketization levels for single-layer and two-layer networks, respectively. This paper proposes construction of a novel class of HPDAs by first constructing a class of PDAs using combinatorial t-designs. The proposed class of HPDAs yields hierarchical coded caching schemes at several memory points for a given number of mirrors and users. Additionally, we introduce the concept of hierarchical memory sharing to achieve the lower envelope of the convex hull of these points. It is shown that the proposed hierarchical schemes have significantly lower subpacketization levels compared to many known schemes. In cases where the system parameters and subpacketization levels of the proposed and existing schemes match, the proposed scheme achieves a better coding delay. Furthermore, the class of PDAs constructed either subsumes several known PDA constructions or achieves a better transmission load for the same system parameters.