On the Optimal Recovery Threshold of Coded Matrix Multiplication - Dutta, Sanghamitra; Fahim, Mohammad; Haddadpour, Farzin; Jeong, Haewon; Cadambe, Viveck; Grover, Pulkit (IEEE transactions on information theory, 2020)
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 m^{2} 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.