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Paper Detail

Paper IDD.3.6
Paper Title Entangled Polynomial Codes for Secure, Private, and Batch Distributed Matrix Multiplication: Breaking the ''Cubic'' Barrier
Authors Qian Yu, Salman Avestimehr, University of Southern California, United States
Session D.3: Distributed Matrix Multiplication
Presentation Lecture
Track Coded and Distributed Computation
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into $m$-by-$p$ and $p$-by-$n$ subblocks, a single multiplication task can be viewed as computing linear combinations of $pmn$ submatrix products, which can be assigned to $pmn$ 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'' ($pmn$) 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, meaning that the final product can be recovered from \emph{any} subset of multiplication results with a size order-wise smaller than $pmn$. In this work, we show that entangled polynomial codes can be further extended to also include these three important settings, and provide a unified framework that order-wise reduces the total computational costs upon the state of the arts by achieving subcubic recovery thresholds.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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