Cache-aided Interference Management Using Hypercube Combinatorial Cache Designs
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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 et al., who proposed a prefetching and a delivery schemes that achieves a sum-DoF of {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 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 et al., or the NMA scheme. When M_TK_T+K_RM_R ≥ K_R, the achievable one-shot sum-DoF using this approach is 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.
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