Coded Computing with Noise

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. We observe that decoding tends to amplify the computation "noise", i.e., the numerical errors at the computation nodes. We use noise amplification as a performance measure to compare various erasure-correction codes, and in particular polynomial codes (which Reed-Solomon codes and other popular codes are a subset of). We show that noise amplification can be significantly reduced by a clever selection of the sampling points and powers of the polynomial code.