Details

Autor(en) / Beteiligte

• Dutta, Sanghamitra
• Fahim, Mohammad
• Haddadpour, Farzin
• Jeong, Haewon
• Cadambe, Viveck
• Grover, Pulkit

Titel

On the Optimal Recovery Threshold of Coded Matrix Multiplication

Ist Teil von

• IEEE transactions on information theory, 2020-01, Vol.66 (1), p.278-301

Ort / Verlag

New York: IEEE

Erscheinungsjahr

2020

Quelle

IEEE Xplore

Beschreibungen/Notizen

• 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 <inline-formula> <tex-math notation="LaTeX">1/m </tex-math></inline-formula> fraction of each matrix can be stored at each worker node, Polynomial codes require <inline-formula> <tex-math notation="LaTeX">m^{2} </tex-math></inline-formula> successful workers, while our MatDot codes only require <inline-formula> <tex-math notation="LaTeX">2m-1 </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> matrices (<inline-formula> <tex-math notation="LaTeX">n \geq 3 </tex-math></inline-formula>) using ideas from MatDot and PolyDot codes.