Distributed Matrix Multiplication Using Group Algebra for On-Device Edge Computing

Leveraging the idea of group theory, we explore the distributed matrix multiplication problem posed in on-device edge computing. We first revisit how to embed matrix multiplication into group structure and then propose a distributed matrix multiplication scheme using the cyclic group. We identify the
condition for the perfect reconstruction
with the proposed scheme, and exhibit that the proposed scheme has better error performance than the uncoded scheme in a noisy channel owing to the diversity gain of the proposed scheme.