Cache-aided Interference Management using Hypercube Combinatorial Cache Design with Reduced Subpacketizations and Order Optimal Sum-Degrees of Freedom
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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 (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 et al., who proposed a scheme that achieves a one-shot sum-DoF of min{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 hypercube. The proposed approach reduces the subpacketization exponentially in terms of K_R M/N and achieves the identical one-shot sum DoF when M_TK_T+K_RM_R/N≤ K_R.
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