Frame Codes For Distributed Coded Computation

TL;DR

This paper introduces a novel polynomial coding scheme inspired by robust frames that reduces noise amplification in distributed coded computation, improving resilience to straggler nodes and enhancing numerical stability.

Contribution

It presents a new polynomial code construction that leverages robust frame theory to mitigate noise amplification in distributed coded computation.

Findings

Reduces noise amplification in decoding process.

Achieves graceful degradation with increasing stragglers.

Improves numerical stability in distributed computation.

Abstract

Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular workaround to the well known ``straggling nodes'' problem, in particular, by matching linear coding for linear computation tasks. It was observed that decoding tends to amplify the computation ``noise'', i.e., the numerical errors at the computation nodes. We propose taking advantage of the case that more nodes return than minimally required. We show how a clever construction of a polynomial code, inspired by recent results on robust frames, can significantly reduce the amplification of noise, and achieves graceful degradation with the number of straggler nodes.