Fundamental Tradeoff Between Computation and Communication With Joint Coding and Interference Management in Wireless Distributed Computing

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.