Masterless Coded Computing: A Fully-Distributed Coded FFT Algorithm

We propose a coded computing strategy for the Fast Fourier Transform (FFT) algorithm in a fully distributed setting, which does not have a powerful master node orches- trating worker nodes. The fully distributed setting requires a large amount of data movements between nodes, and this communication is often the bottleneck in parallel computing. We identify communication cost of each step of the coded FFT algorithm using the $\alpha -\beta $ model, which is commonly used in high- performance computing literature to estimate communication latency. We show that by using $\mathrm {a} (P,~K)$ systematic MDS code, the communication overhead of coding is negligible in comparison to the communication costs inherent in the uncoded FFT implementation if $P-K=o(\log K)$.