On the Optimal Recovery Threshold of Coded Matrix Multiplication

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

Research output: Contribution to journalArticlepeer-review

145 Scopus citations


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.

Original languageEnglish (US)
Article number8765375
Pages (from-to)278-301
Number of pages24
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2020

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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