An Optimal Coded Matrix Multiplication Scheme for Leveraging Partial Stragglers.

The majority of prior coded computation works treat stragglers as erasures over an erasure channel and ignore their partial computations. The whole speed of a computation network will still be limited due to different processing speeds of worker nodes. This paper presents a novel coded scheme for this problem to effectively leverage partial stragglers. It simultaneously embeds the maximum distance separable (MDS) codes and codes in the universally decodable matrices (UDMs) into the system. By imposing constraints on coding parameters, the coefficient matrix corresponding to any first k A k B products of encoded submatrices from worker nodes is full rank, when two input matrices are partitioned into k A and k B block-columns, respectively. Thus, it only requires the minimum k A k B products performed by worker nodes (including stragglers). Analysis results show that our scheme can achieve not only the optimal utilization of partial computations of worker nodes, but also the optimal straggler resilience capability.