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This paper considers the problem of calculating the matrix multiplication oftwo massive matrices $\mathbf{A}$ and $\mathbf{B}$ distributedly. We provide amodulo technique that can be applied to coded distributed matrix multiplicationproblems to reduce the recovery threshold. This technique exploits the specialstructure of interpolation points and can be applied to many existing codedmatrix designs. Recently studied discrete Fourier transform based code achievesa smaller recovery threshold than the optimal MatDot code with the expense thatit cannot resist stragglers. We also propose a distributed matrixmultiplication scheme based on the idea of locally repairable code to reducethe recovery threshold of MatDot code and provide resilience to stragglers. Wealso apply our constructions to a type of matrix computing problems, wheregeneralized linear models act as a special case.

Distributed Matrix Multiplication with a Smaller Recovery Threshold through Modulo-based Approaches