In this paper, we investigate the fundamental tradeoff between computation and communication for the full-duplex (FD) wireless MapReduce distributed computing network. Specifically, a coded interference alignment and neutralization (CIAN) scheme is proposed to significantly reduce the achievable normalized delivery time (NDT) for any given computation load, which jointly exploits both the coding and interference management technologies. In particular, a novel coding strategy is designed to create the coded message desired by multiple nodes, thereby providing the coded multicasting gain. Furthermore, the Shuffle phase is molded as a special cooperative X-multicast network. For this network, a novel IAN scheme is proposed to improve the achievable sum degree of freedom (SDoF), thereby providing the IAN gain. In the proposed CIAN scheme, the fundamental tradeoff between the coded multicasting gain and IAN gain is characterized, and the achievable NDT is minimized by carefully optimizing these two gains. Furthermore, a tight information-theoretic lower bound on the NDT is derived, demonstrating the optimality of the CIAN scheme in some cases. In other cases, the achievable NDT of the CIAN scheme and the lower bound are within a multiplicative gap of 2. Theoretical analysis and numerical results indicate the superior performance of the CIAN scheme compared to existing schemes, particularly by providing additional coded multicasting gain and improved IAN gain.

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.