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We introduce two generalizations to the paradigm of using Random Khatri-RaoProduct (RKRP) codes for distributed matrix multiplication. We first introducea class of codes called Sparse Random Khatri-Rao Product (SRKRP) codes whichhave sparse generator matrices. SRKRP codes result in lower encoding,computation and communication costs than RKRP codes when the input matrices aresparse, while they exhibit similar numerical stability to other state of theart schemes. We empirically study the relationship between the probability ofthe generator matrix (restricted to the set of non-stragglers) of a randomlychosen SRKRP code being rank deficient and various parameters of the codingscheme including the degree of sparsity of the generator matrix and the numberof non-stragglers. Secondly, we show that if the master node can perform a verysmall number of matrix product computations in addition to the computationsperformed by the workers, the failure probability can be substantiallyimproved.

Sparse Random Khatri-Rao Product Codes for Distributed Matrix Multiplication