Towards Practical File Packetizations in Wireless Device-to-Device Caching Networks

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.Comment: 32 pages, 5 figure

Cache-aided Interference Management using Hypercube Combinatorial Cache Design with Reduced Subpacketizations and Order Optimal Sum-Degrees of Freedom

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 (AWGN) 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 with one-shot transmission was firstly investigated by Naderializadeh {\em et al.}, who proposed a scheme that achieves a one-shot sum-DoF of $\min\{\frac{{M_TK_T+K_RM_R}}{{N}}, K_R\}$, which is optimal within a constant of $2$. One of the biggest limitations of this scheme is the requirement of high subpacketization level. This paper attempts to design new algorithms to reduce the file subpacketization in such a network without hurting the sum-DoF. In particular, we propose a new approach for both prefetching and linearly coded delivery based on a combinatorial design called {\em hypercube}. The proposed approach reduces the subpacketization exponentially in terms of $K_R M/N$ and achieves the identical one-shot sum DoF when $\frac{M_TK_T+K_RM_R}{N} \leq K_R$.Comment: arXiv admin note: substantial text overlap with arXiv:1902.0013