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arXiv · 2006.08911

Multilinear Algebra for Distributed Storage

Iwan Duursma·Xiao Li·Hsin-Po Wang
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Abstract

An $(n, k, d, \alpha, \beta, M)$-ERRC (exact-repair regenerating code) is a collection of $n$ nodes used to store a file. For a file of total size $M$, each node stores $\alpha$ symbols, any $k$ nodes recover the file, and any $d$ nodes repair any other node via sending out $\beta$ symbols. We establish a multilinear algebra foundation to assemble $(n, k, d, \alpha, \beta, M)$-ERRCs for all meaningful $(n, k, d)$ tuples. Our ERRCs tie the $\alpha/M$-versus-$\beta/M$ trade-off with cascade codes, the best known construction for this trade-off. We give directions on how these ERRCs repair multiple failures.

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Iwan Duursma, Xiao Li, Hsin-Po Wang. 2020-06-16. Multilinear Algebra for Distributed Storage. https://doi.org/10.1137/20m1346742

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