Some new Constructions of Coded Caching Schemes with Reduced Subpacketization

Abstract: We study the problem of constructing centralized coded caching schemes with low subpacketization level based on the placement delivery array (PDA) design framework. PDA design is an efficient way to construct centralized coded caching schemes and most existing schemes, including the famous Maddah-Ali-Niesen scheme, can be described using PDA. In this paper, we first prove that constructing a PDA is equivalent to constructing three binary matrices that satisfy certain conditions. From this perspective, we then propose some new constructions of coded caching schemes using PDA design based on projective geometries over finite fields, combinatorial configurations, and t-designs, respectively. Our constructions achieve low subpacketization level (e.g., linear subpacketization) with reasonable rate loss and include several known results as special cases. Finally, we give an approach to construct new coded caching scheme from existing schemes based on direct product of PDAs. Our results enrich the coded caching schemes of low subpacketization level.