Extended Placement Delivery Arrays for Multi-Antenna Coded Caching Scheme

This work addresses the multi-antenna coded caching problem where a server with L transmit antennas communicates to K users through a wireless broadcast link. In the problem setting, the server has a library of N files, and each user is equipped with a dedicated cache of capacity M . A novel solution for the multi-antenna coded caching problem is obtained by designing a combinatorial structure called an extended placement delivery array (EPDA). It is shown that the placement delivery arrays known for the centralized coded caching scheme are a special class of EPDAs with L = 1. Furthermore, three constructions of EPDAs are proposed for the settings: a) K = t + L , b) K = nt + ( n - 1) L ; L ≥ t, n ≥ 2, and c) K, L, t such that t + L ≤ K , where t = KM/N is an integer. The multi-antenna schemes resulting from the first two constructions achieve the optimal degrees of freedom (DoF) t + L with a subpacketization number -the number of subfiles into which a file is divided- K /gcd( K, t,L ), which is lower than the subpacketization number of the existing schemes. The scheme obtained from the third construction also achieves the optimal DoF with a subpacketization number ( K /γ ( t + L )/γ) ( t + L )/γ, where γ = gcd( K, t,L ).