# Universally Decodable Matrices for Distributed Matrix-Vector Multiplication

## TL;DR

This paper introduces a novel class of distributed matrix-vector multiplication schemes using universally decodable matrices and Rosenbloom-Tsfasman codes, effectively leveraging partial computations and ensuring numerical stability.

## Contribution

It presents a new coding scheme for distributed matrix-vector multiplication that accounts for computation order and partial results, enhancing efficiency and stability.

## Key findings

- Effective mitigation of stragglers in distributed computation
- Sparse and numerically stable coding schemes
- Experimental validation of scheme effectiveness

## Abstract

Coded computation is an emerging research area that leverages concepts from erasure coding to mitigate the effect of stragglers (slow nodes) in distributed computation clusters, especially for matrix computation problems. In this work, we present a class of distributed matrix-vector multiplication schemes that are based on codes in the Rosenbloom-Tsfasman metric and universally decodable matrices. Our schemes take into account the inherent computation order within a worker node. In particular, they allow us to effectively leverage partial computations performed by stragglers (a feature that many prior works lack). An additional main contribution of our work is a companion matrix-based embedding of these codes that allows us to obtain sparse and numerically stable schemes for the problem at hand. Experimental results confirm the effectiveness of our techniques.