TY - JOUR
T1 - On the Optimal Recovery Threshold of Coded Matrix Multiplication
AU - Dutta, Sanghamitra
AU - Fahim, Mohammad
AU - Haddadpour, Farzin
AU - Jeong, Haewon
AU - Cadambe, Viveck
AU - Grover, Pulkit
N1 - Funding Information:
Manuscript received May 14, 2018; revised April 16, 2019; accepted May 11, 2019. Date of publication July 17, 2019; date of current version December 23, 2019. This work was supported in part by the Systems on Nanoscale Information fabriCs (SONIC) and in part by the NSF Awards under Grant CCF-1350314, Grant CCF-1464336, Grant CCF-1553248, Grant CNS-1702694, and Grant 1763657. This work was presented in part at the 2017 Annual Allerton Conference on Communication, Control, and Computing.
Funding Information:
This work was supported in part by the Systems on Nanoscale Information fabriCs (SONIC) and in part by the NSF Awards under Grant CCF-1350314, Grant CCF-1464336, Grant CCF-1553248, Grant CNS-1702694, and Grant 1763657.
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2020/1
Y1 - 2020/1
N2 - 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.
AB - 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.
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U2 - 10.1109/TIT.2019.2929328
DO - 10.1109/TIT.2019.2929328
M3 - Article
AN - SCOPUS:85077226827
VL - 66
SP - 278
EP - 301
JO - IRE Professional Group on Information Theory
JF - IRE Professional Group on Information Theory
SN - 0018-9448
IS - 1
M1 - 8765375
ER -