On Allocation of Systematic Blocks in Coded Distributed Computing

Abstract

Coded distributed computing is used to mitigate the adverse effect of slow workers on the computation time in distributed computing systems. However, using error-correction codes results in encoding and decoding delays. In this work, we consider a systematic maximum-distance separable (MDS) coded matrix-vector multiplication problem with multi-message communication (MMC), where the master assigns multiple sub-tasks to each worker. In this setup, we show that the received systematic outputs can be used to reduce the decoding time by implementing a proper decoding algorithm. To further reduce the decoding time, we use the MMC property that sub-tasks are executed sequentially to propose an allocation of the systematic sub-tasks that significantly increases the number of received systematic outputs. Our results further demonstrate that the reduction in the decoding time is even more significant in applications that require only a partial recovery. In these applications, it suffices to complete a certain percentage of the computation, and using our approach, we show that decoding may be completely avoided.