  We consider wireless device-to-device (D2D) caching networks with single-hop
transmissions. Previous work has demonstrated that caching and coded
multicasting can significantly increase per user throughput. However, the
state-of-the-art coded caching schemes for D2D networks are generally
impractical because content files are partitioned into an exponential number of
packets with respect to the number of users if both library and memory sizes
are fixed. In this paper, we present two combinatorial approaches of D2D coded
caching network design with reduced packetizations and desired throughput gain
compared to the conventional uncoded unicasting. The first approach uses a
"hypercube" design, where each user caches a "hyperplane" in this hypercube and
the intersections of "hyperplanes" represent coded multicasting codewords. In
addition, we extend the hypercube approach to a decentralized design. The
second approach uses the Ruzsa-Szem\'eredi graph to define the cache placement.
Disjoint matchings on this graph represent coded multicasting codewords. Both
approaches yield an exponential reduction of packetizations while providing a
per-user throughput that is comparable to the state-of-the-art designs in the
literature. Furthermore, we apply spatial reuse to the new D2D network designs
to further reduce the required packetizations and significantly improve per
user throughput for some parameter regimes.
