On the Optimal Recovery Threshold of Coded Matrix Multiplication

We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent "Polynomial code" constructions in recovery threshold, i. e., the required number of successful workers. When m-th fraction of each matrix can be stored in each worker node, polynomial codes require m(2) successful workers, while our novel MatDot codes only require 2m - 1 successful workers, albeit at a higher communication cost from each worker to the fusion node. Further, we propose " PolyDot" coding that interpolates between Polynomial codes and MatDot codes. Finally, we demonstrate an application of PolyDot codes to multiplying multiple (> 2) matrices.