Wireless Distributed Computing Networks with Interference Alignment and Neutralization

In this paper, for a general full-duplex wireless MapReduce distributed computing network, we investigate the minimization of the communication overhead for a given computation overhead. The wireless MapReduce framework consists of three phases: Map phase, Shuffle phase and Reduce phase. Specifically, we model the Shuffle phase into a cooperative X network based on a more general file assignment strategy. Furthermore, for this cooperative X network, we derive an information-Theoretic upper bound on the sum degree of freedom (SDoF). Moreover, we propose a joint interference alignment and neutralization (IAN) scheme to characterize the achievable SDoF. Especially, in some cases, the achievable SDoF coincides with the upper bound on the SDoF, hence, the IAN scheme provides the optimal SDoF. Finally, based on the SDoF, we present an information-Theoretic lower bound on the normalized delivery time (NDT) and achievable NDT of the wireless distributed computing network, which are less than or equal to those of the existing networks. The lower bound on the NDT shows that 1) there is a tradeoff between the computation load and the NDT; 2) the achievable NDT is optimal in some cases, hence, the proposed IAN scheme can reduce the communication overhead effectively.