  We consider a cache-aided interference network which consists of a library of
$N$ files, $K_T$ transmitters and $K_R$ receivers (users), each equipped with a
local cache of size $M_T$ and $M_R$ files respectively, and connected via a
discrete-time additive white Gaussian noise channel. Each receiver requests an
arbitrary file from the library. The objective is to design a cache placement
without knowing the receivers' requests and a communication scheme such that
the sum Degrees of Freedom (sum-DoF) of the delivery is maximized. This network
model has been investigated by Naderializadeh {\em et al.}, who proposed a
prefetching and a delivery schemes that achieves a sum-DoF of
$\min\{\frac{{M_TK_T+K_RM_R}}{{N}}, K_R\}$. One of biggest limitations of this
scheme is the requirement of high subpacketization level. This paper is the
first attempt in the literature (according to our knowledge) to reduce the file
subpacketization in such a network. In particular, we propose a new approach
for both prefetching and linear delivery schemes based on a combinatorial
design called {\em hypercube}. We show that required number of packets per file
can be exponentially reduced compared to the state of the art scheme proposed
by Naderializadeh {\em et al.}, or the NMA scheme. When $M_TK_T+K_RM_R \geq
K_R$, the achievable one-shot sum-DoF using this approach is
$\frac{{M_TK_T+K_RM_R}}{{N}}$ , which shows that 1) the one-shot sum-DoF scales
linearly with the aggregate cache size in the network and 2) it is within a
factor of $2$ to the information-theoretic optimum. Surprisingly, the identical
and near optimal sum-DoF performance can be achieved using the hypercube
approach with a much less file subpacketization.
