# Coded Distributed Computing over Packet Erasure Channels

## TL;DR

This paper analyzes the impact of packet erasure channels on coded distributed computing, deriving bounds on latency and proposing optimized coding strategies under link failure conditions.

## Contribution

It models link failures as packet erasures in coded distributed computing, providing bounds on latency and design guidelines for MDS codes considering retransmission limits.

## Key findings

- Derived closed-form bounds on latency under packet erasures.
- Provided design guidelines for MDS codes based on erasure probability.
- Analyzed the trade-offs between latency, bandwidth, and success probability.

## Abstract

Coded computation is a framework which provides redundancy in distributed computing systems to speed up largescale tasks. Although most existing works assume an error-free scenarios in a master-worker setup, the link failures are common in current wired/wireless networks. In this paper, we consider the straggler problem in coded distributed computing with link failures, by modeling the links between the master node and worker nodes as packet erasure channels. When the master fails to detect the received signal, retransmission is required for each worker which increases the overall run-time to finish the task. We first investigate the expected overall run-time in this setting using an (n; k) maximum distance separable (MDS) code. We obtain the lower and upper bounds on the latency in closed-forms and give guidelines to design MDS code depending on the packet erasure probability. Finally, we consider a setup where the number of retransmissions is limited due to the bandwidth constraint. By formulating practical optimization problems related to latency, transmission bandwidth and probability of successful computation, we obtain achievable performance curves as a function of packet erasure probability.