On the Optimal Recovery Threshold of Coded Matrix Multiplication | IEEE Journals & Magazine | IEEE Xplore

On the Optimal Recovery Threshold of Coded Matrix Multiplication


Abstract:

We provide novel coded computation strategies for distributed matrix-matrix products that outperform the recent “Polynomial code” constructions in recovery threshold, i.e...Show More

Abstract:

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.
Published in: IEEE Transactions on Information Theory ( Volume: 66, Issue: 1, January 2020)
Page(s): 278 - 301
Date of Publication: 17 July 2019

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