Coded Computing for Resilient, Secure, and Privacy-Preserving Distributed Matrix Multiplication

Coded computing is a new framework to address fundamental issues in large scale distributed computing, by injecting structured randomness and redundancy. We first provide an overview of coded computing and summarize some recent advances. Then we focus on distributed matrix multiplication and conside...

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Vydané v:IEEE transactions on communications Ročník 69; číslo 1; s. 59 - 72
Hlavní autori: Yu, Qian, Avestimehr, A. Salman
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.01.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
batch processing
coding theory
Computer networks
Computing costs
Data privacy
Decoding
Distributed computing
Distributed processing
Encoding
Matrices (mathematics)
matrix multiplication
Multiplication
Partitioning
Polynomials
Privacy
Recovery
Redundancy
Resilience
Security
stragglers
Task analysis
ISSN:0090-6778, 1558-0857
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Shrnutí:Coded computing is a new framework to address fundamental issues in large scale distributed computing, by injecting structured randomness and redundancy. We first provide an overview of coded computing and summarize some recent advances. Then we focus on distributed matrix multiplication and consider a common scenario where each worker is assigned a fraction of the multiplication task. In particular, by partitioning two input matrices into <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula>-by-<inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula>-by-<inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> subblocks, a single multiplication task can be viewed as computing linear combinations of <inline-formula> <tex-math notation="LaTeX">pmn </tex-math></inline-formula> submatrix products, which can be assigned to <inline-formula> <tex-math notation="LaTeX">pmn </tex-math></inline-formula> workers. Such block-partitioning-based designs have been widely studied under the topics of secure, private, and batch computation, where the state of the arts all require computing at least "cubic" (<inline-formula> <tex-math notation="LaTeX">pmn </tex-math></inline-formula>) number of submatrix multiplications. Entangled polynomial codes, first presented for straggler mitigation, provides a powerful method for breaking the cubic barrier. It achieves a subcubic recovery threshold, i.e., recovering the final product from any subset of multiplication results with a size order-wise smaller than <inline-formula> <tex-math notation="LaTeX">pmn </tex-math></inline-formula>. We show that entangled polynomial codes can be further extended to also include these three important settings, providing unified frameworks that order-wise reduce the total computational costs by achieving subcubic recovery thresholds.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2020.3032196