Code Design and Latency Analysis of Distributed Matrix Multiplication with Straggling Servers in Fading Channels

This paper exploits coding to speed up computation offloading in a multi-server mobile edge computing(MEC) network with straggling servers and channel fading. The specific task we consider is to compute the product between a user-generated input data matrix and a large-scale model matrix that is stored distributively across the multiple edge nodes.The key idea of coding is to introduce computation redundancy to improve robustness against straggling servers and to create communication redundancy to improve reliability against channel fading. We utilize the hybrid design of maximum distance separable(MDS) coding and repetition coding. Based on the hybrid coding scheme, we conduct theoretical analysis on the average task uploading time, average edge computing time, and average output downloading time, respectively and then obtain the end-to-end task execution time. Numerical results demonstrate that when the task uploading phase or the edge computing phase is the performance bottleneck, the hybrid coding reduces to MDS coding; when the downlink transmission is the bottleneck, the hybrid coding reduces to repetition coding. The hybrid coding also outperforms the entangled polynomial coding that causes higher uplink and downlink communication loads.