Extended Placement Delivery Arrays for Multi-Antenna Coded Caching Scheme

Abstract

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 multiantenna 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 $\frac{M}{N} = \frac{Z}{F}$, and the delivery time $T = \frac{S}{F}$. The placement delivery array (for single-antenna coded caching scheme) is a special class of EPDAs with L = 1. For the multiantenna 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 $t = \frac{{KM}}{N}$ 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 $\frac{K}{{\gcd (K,t,L)}}$. This subpacketization number is less than that required by previously known schemes in the literature.