Wireless Multihop Device-to-Device Caching Networks

We consider a wireless device-to-device network, where n nodes are uniformly distributed at random over the network area. We let each node caches M files from a library of size m ??= M. Each node in the network requests a file from the library independently at random, according to a popularity distribution, and is served by other nodes having the requested file in their local cache via (possibly) multihop transmissions. Under the classical "protocol model" of wireless networks, we characterize the optimal per-node capacity scaling law for a broad class of heavy-tailed popularity distributions, including Zipf distributions with exponent less than one. In the parameter regime of interest, i.e., m = o(nM), we show that a decentralized random caching strategy with uniform probability over the library yields the optimal per-node capacity scaling of Theta(root M/m) for heavy-tailed popularity distributions. This scaling is constant with n, thus yielding throughput scalability with the network size. Furthermore, the multihop capacity scaling can be significantly better than for the case of single-hop caching networks, for which the per-node capacity is Theta(M/m). The multihop capacity scaling law can be further improved for a Zipf distribution with exponent larger than some threshold ??1, by using a decentralized random caching uniformly across a subset of most popular files in the library. Namely, ignoring a subset of less popular files (i.e., effectively reducing the size of the library) can significantly improve the throughput scaling while guaranteeing that all nodes will be served with high probability as n increases.S.-W. Jeon was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology under Grant NRF-2013R1A1A1064955. G. Caire was supported in part by the Alexander von Humboldt Professorship and in part by NSF under Grant 1161801. A. F. Molisch was supported by NSF under Award CCF-1423140. This paper was presented at the 2015 IEEE Information Theory Workshop and the 2015 IEEE International Conference on Communications