Fundamental Limits of Coded Linear Transform

TL;DR

This paper introduces a novel coded computation strategy called diagonal code for distributed linear transforms, achieving optimal recovery threshold and load, with additional random codes offering high-probability guarantees and improved efficiency.

Contribution

The paper presents the first code achieving simultaneous optimal recovery threshold and computation load in distributed linear transforms, along with new random codes that improve efficiency.

Findings

Diagonal code achieves optimal recovery threshold and load.

Random codes guarantee high-probability optimal recovery with less computation.

Experimental results outperform existing schemes.

Abstract

In large scale distributed linear transform problems, coded computation plays an important role to effectively deal with "stragglers" (distributed computations that may get delayed due to few slow or faulty processors). We propose a coded computation strategy, referred to as diagonal code, that achieves the optimum recovery threshold and the optimum computation load. This is the first code that simultaneously achieves two-fold optimality in coded distributed linear transforms. Furthermore, by leveraging the idea from random proposal graph theory, we design two random codes that can guarantee optimum recovery threshold with high probability but with much less computation load. These codes provide order-wise improvement over the state-of-the-art. Moreover, the experimental results show significant improvement compared to both uncoded and existing coding schemes.