We introduce two generalizations to the paradigm of using Random Khatri-Rao Product (RKRP) codes for distributed matrix multiplication. We first introduce a class of codes called Sparse Random Khatri-Rao Product (SRKRP) codes which have sparse generator matrices. SRKRP codes result in lower encoding, computation and communication costs than RKRP codes when the input matrices are sparse, while they exhibit similar numerical stability to other state of the art schemes. We empirically study the relationship between the probability of the generator matrix (restricted to the set of non-stragglers) of a randomly chosen SRKRP code being rank deficient and various parameters of the coding scheme including the degree of sparsity of the generator matrix and the number of non-stragglers. Secondly, we show that if the master node can perform a very small number of matrix product computations in addition to the computations performed by the workers, the failure probability can be substantially improved.

We introduce a class of codes, called Squeezed Random Khatri-Rao Product (RKRP) codes, for coded matrix multiplication when each worker node can perform multiple submatrix products. The proposed codes are a generalization of RKRP codes in [1] and are built on the idea of squeezed polynomial codes in [2]. We show that squeezed RKRP codes are maximum distance separable with probability 1. They have the same communication cost as that of squeezed polynomial codes while offering better numerical stability.