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)
$K = nt+ (n-1)L;L\geq t, n\geq 2$
, and c)
$K,L,t$
such that
$t + L\leq K$
, 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-
$K/\text {gcd}(K,t,L)$
, 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
$\binom {K/{\gamma }}{(t+L)/{\gamma }}\left ({{t+L}}\right)/{\gamma }$
, where
$\gamma =\text {gcd}(K,t,L)$
.