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/gamma)((t+L)/gamma))(t+L)/gamma , where gamma=gcd(K,t,L)