Structured Polynomial Codes for Distributed Matrix Multiplication

Abstract

We consider the practical source-worker-receiver framework for distributed matrix multiplication over finite fields. In a setting with two distributed sources with separate encoders, with the first source having access to A and the second to B, with $I$ distributed workers, where each has a bounded storage (memory) capability reflecting a bounded computational capability, and thus can multiply matrices of smaller size, and one receiver, which aims to reconstruct ${\mathbf { A}}^{\intercal }{\mathbf { B}}$ from the transmissions of workers. By combining a structured linear encoding scheme with the polynomial code framework, we introduce a novel class of structured polynomial codes (StPolyDot codes) for distributed matrix multiplication, leveraging the bilinear structure of this problem, and show that our codes can surpass the performance of the existing state of art in terms of both memory and communication costs, while also maintaining certain advantages in terms of security.