Coded FFT and Its Communication Overhead

TL;DR

This paper introduces a coded computing approach for distributed FFT that uses MDS codes to achieve error resilience with minimal additional communication overhead, especially when the number of parity nodes is small.

Contribution

It applies systematic MDS codes to distributed FFT, demonstrating negligible communication overhead compared to uncoded FFT when parity nodes are few.

Findings

Coded FFT with MDS codes is resilient to errors during distributed computation.

Communication overhead of coding is negligible if parity nodes are at most o(log K).

The approach improves fault tolerance with minimal extra communication.

Abstract

We propose a coded computing strategy and examine communication costs of coded computing algorithms to make distributed Fast Fourier Transform (FFT) resilient to errors during the computation. We apply maximum distance separable (MDS) codes to a widely used "Transpose" algorithm for parallel FFT. In the uncoded distributed FFT algorithm, the most expensive step is a single "all-to-all" communication. We compare this with communication overhead of coding in our coded FFT algorithm. We show that by using a systematic MDS code, the communication overhead of coding is negligible in comparison with the communication costs inherent in an uncoded FFT implementation if the number of parity nodes is at most $o(\log K)$, where $K$ is the number of systematic nodes.