Codes for Distributed Finite Alphabet Matrix-Vector Multiplication

Recent work has developed coding theoretic approaches to add redundancy to distributed matrix-vector multiplications with the goal of speeding up the computation by mitigating the straggler effect in distributed computing. In this paper, we consider the case where the matrix comes from a small (e.g., binary) alphabet, where a variant of a popular method called the “Four-Russians method” is known to have significantly lower computational complexity as compared with the usual matrix-vector multiplication algorithm. We develop novel code constructions that are applicable to binary matrix-vector multiplication via a variant of the Four-Russians method called the Mailman algorithm. Specifically, in our constructions, the encoded matrices have a low alphabet that ensures lower computational complexity, as well as good straggler tolerance. We also present a trade-off between the communication and computation cost of distributed coded matrix-vector multiplication for general, possibly non-binary, matrices.