Extended Placement Delivery Arrays for Multi-Antenna Coded Caching Scheme
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The multi-antenna coded caching problem, where the server having L transmit antennas communicating to K users through a wireless broadcast link, is addressed. In the problem setting, the server has a library of N files, and each user is equipped with a dedicated cache of capacity M. The idea of extended placement delivery array (EPDA), an array which consists of a special symbol ⋆ and integers in a set {1,2,…,S}, is proposed to obtain a novel solution for the aforementioned multi-antenna coded caching problem. From a (K,L,F,Z,S) EPDA, a multi-antenna coded caching scheme with K users, and the server with L transmit antennas, can be obtained in which the normalized memory M/N=Z/F, and the delivery time T=S/F. The placement delivery array (for single-antenna coded caching scheme) is a special class of EPDAs with L=1. For the multi-antenna coded caching schemes constructed from EPDAs, it is shown that the maximum possible Degree of Freedom (DoF) that can be achieved is t+L, where t=KM/N is an integer. Furthermore, two constructions of EPDAs are proposed: a) K=t+L, and b) K=nt+(n-1)L, L≥ t, where n≥ 2 is an integer. In the resulting multi-antenna schemes from those EPDAs achieve the full DoF, while requiring a subpacketization number K/gcd(K,t,L). This subpacketization number is less than that required by previously known schemes in the literature.
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