Coded Real Number Matrix Multiplication for On-Device Edge Computing

Zhiquan Tan, Dingli Yuan, Yifan Zhang, Zhongyi Huang

Abstract: This letter addresses the challenge of multiplying large real-numbered matrices $\mathbf {A}$ and $\mathbf {B}$ in on-device edge computing environments with a master node and $N$ worker nodes. To ensure accuracy and mitigate adversarial behavior, existing approaches rely on polynomial coding techniques. However, polynomial decoding on real numbers is numerically unstable, leading prior works to employ finite fields or complex number fields. Nevertheless, computing on finite fields may encounter computation overflows. In this letter, we propose a novel, numerically stable coded matrix multiplication scheme on real number fields. Our approach detects malicious workers and mitigates the impact of slower workers (stragglers), all while operating solely on real number fields.

External IDs:dblp:journals/spl/TanYZH23