On the Optimal Recovery Threshold of Coded Matrix Multiplication

We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent 'Polynomial code' constructions in recovery threshold, i.e., the required number of successful workers. When a fixed 1/m fraction of each matrix can be stored at each worker node, Polynomial codes require m2 successful workers, while our MatDot codes only require 2m-1 successful workers. However, MatDot codes have higher computation cost per worker and higher communication cost from each worker to the fusion node. We also provide a systematic construction of MatDot codes. Furthermore, we propose 'PolyDot' coding that interpolates between Polynomial codes and MatDot codes to trade off computation/communication costs and recovery thresholds. Finally, we demonstrate a novel coding technique for multiplying n matrices (n ≥ 3) using ideas from MatDot and PolyDot codes.