# Coded Matrix Multiplication on a Group-Based Model

## TL;DR

This paper introduces a group-based coding scheme for distributed matrix multiplication that models real-world server clusters, achieving near-optimal performance and reduced decoding complexity.

## Contribution

It proposes a novel group code tailored for clustered distributed systems, reflecting practical conditions and improving decoding efficiency.

## Key findings

- Achieves asymptotic optimality in large-scale regimes.
- Demonstrates near-optimal performance for finite system sizes.
- Reduces decoding complexity through parallel decoding.

## Abstract

Coded distributed computing has been considered as a promising technique which makes large-scale systems robust to the "straggler" workers. Yet, practical system models for distributed computing have not been available that reflect the clustered or grouped structure of real-world computing servers. Neither the large variations in the computing power and bandwidth capabilities across different servers have been properly modeled. We suggest a group-based model to reflect practical conditions and develop an appropriate coding scheme for this model. The suggested code, called group code, employs parallel encoding for each group. We show that the suggested coding scheme can asymptotically achieve optimal computing time in regimes of infinite n, the number of workers. While theoretical analysis is conducted in the asymptotic regime, numerical results also show that the suggested scheme achieves near-optimal computing time for any finite but reasonably large n. Moreover, we demonstrate that the decoding complexity of the suggested scheme is significantly reduced by the virtue of parallel decoding.