# Distributed Matrix-Vector Multiplication: A Convolutional Coding Approach

## TL;DR

This paper introduces a convolutional coding approach for distributed matrix-vector multiplication that effectively mitigates stragglers, offers low-complexity decoding, and is well-suited for sparse matrices, outperforming Reed-Solomon based methods.

## Contribution

The paper presents a novel convolutional coding scheme for distributed matrix-vector multiplication with low-complexity decoding and improved numerical stability over Reed-Solomon codes.

## Key findings

- Peeling decoder enables efficient recovery.
- Scheme is numerically more stable.
- Performs well with sparse matrices.

## Abstract

Distributed computing systems are well-known to suffer from the problem of slow or failed nodes; these are referred to as stragglers. Straggler mitigation (for distributed matrix computations) has recently been investigated from the standpoint of erasure coding in several works. In this work we present a strategy for distributed matrix-vector multiplication based on convolutional coding. Our scheme can be decoded using a low-complexity peeling decoder. The recovery process enjoys excellent numerical stability as compared to Reed-Solomon coding based approaches (which exhibit significant problems owing their badly conditioned decoding matrices). Finally, our schemes are better matched to the practically important case of sparse matrix-vector multiplication as compared to many previous schemes. Extensive simulation results corroborate our findings.