Coded Matrix Computation in Wireless Network

Despite its vital role in intelligent IoT networks, distributed computing was not studied well in wireless networks. Notably, the distortions introduced by wireless channels and noise can significantly undermine the accuracy of distributed computations. Unfortunately, existing distributed computing schemes inadequately address this critical issue. In this paper, we aim at resolving the numerical stability issue associated within wireless networks and building a new computationally accurate design framework which concretely integrates distributed computing and communication. To this end, we first explore the previous group algebra based coded matrix computation scheme, suitable for numerically stable computation in noisy network, in orthogonal multiple access channel and perform a thorough analysis of computational errors. Furthermore, to leverage the inherent communication structure constructed in distributed computing and thus more efficiently utilize limited wireless resources, we propose to combine the Compute-and-Forward scheme with coded matrix computation. Furthermore, we devise a novel transmission scheme for distributed computing called the Broadcast-and-Compute scheme, in which a master node broadcasts the same information, not transmitting differently encoded submatrices to worker nodes. We analyze the computation errors of Compute-and-Forward and Broadcast-and-Compute based coded matrix computation. The superiority of the proposed schemes is validated by various simulations.