Code design and latency analysis of distributed matrix multiplication with straggling servers in fading channels
페이딩 채널에서 지연 서버를 사용한 분산 행렬 곱셈의 코드 설계 및 대기 시간 분석
Diseño de código y análisis de latencia de la multiplicación de matrices distribuidas con servidores rezagados en canales que se desvanecen
Conception de code et analyse de latence de la multiplication matricielle distribuée avec des serveurs errants dans des canaux en déclin
Разработка кода и анализ задержки при распределенном умножении матриц с неравномерными серверами в каналах с замиранием
Ning Liu ¹, Kuikui Li 李奎奎 ², Meixia Tao 陶梅霞 ³
¹ School of Electronics, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
中国 上海 上海交通大学电子信息与电气工程学院
² Huawei Technologies Co., Ltd., Shanghai 201206, China
中国 上海 华为技术有限公司
³ Department of Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
中国 上海 上海交通大学电子工程系
China Communications, 13 November 2021

This paper exploits coding to speed up computation offloading in a multi-server mobile edge computing (MEC) network with straggling servers and channel fading. The specific task we consider is to compute the product between a user-generated input data matrix and a large-scale model matrix that is stored distributively across the multiple edge nodes.

The key idea of coding is to introduce computation redundancy to improve robustness against straggling servers and to create communication redundancy to improve reliability against channel fading. We utilize the hybrid design of maximum distance separable (MDS) coding and repetition coding. Based on the hybrid coding scheme, we conduct theoretical analysis on the average task uploading time, average edge computing time, and average output downloading time, respectively and then obtain the end-to-end task execution time.

Numerical results demonstrate that when the task uploading phase or the edge computing phase is the performance bottleneck, the hybrid coding reduces to MDS coding; when the downlink transmission is the bottleneck, the hybrid coding reduces to repetition coding. The hybrid coding also outperforms the entangled polynomial coding that causes higher uplink and downlink communication loads.
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