PDA Construction via Union of Cartesian Product Cache Configurations for Coded Caching

Caching is an efficient technique to reduce peak traffic by storing popular content in local caches. Placement delivery array (PDA) proposed by Yan et al. is a combinatorial structure to design coded caching schemes with uncoded placement and one-shot linear delivery. By taking the $m$-fold Cartesian product of a small base PDA, Wang et al. constructed a big PDA while maintaining the memory ratio and transmission load unchanged, which achieves linear growth in both the number of users and coded caching gain. In order to achieve exponential growth in both the number of users and coded caching gain, in this paper we propose a PDA construction by taking the union operation of the cache configurations from the $m$-fold Cartesian product of a base PDA. The resulting PDA leads to a coded caching scheme with subpacketization increasing sub-exponentially with the number of users while keeping the load constant for fixed memory ratio. By applying the proposed construction to existing base PDAs, three new coded caching schemes are obtained, which cover some existing schemes as special cases and can achieve lower load with simultaneously lower subpacketization for some memory ratios.