TY - JOUR

T1 - Multilinear algebra for minimum storage regenerating codes

T2 - a generalization of the product-matrix construction

AU - Duursma, Iwan

AU - Wang, Hsin Po

N1 - Funding Information:
This work was partially supported by NSF Grant CCF-1619189.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2021

Y1 - 2021

N2 - An (n, k, d, α) -MSR (minimum storage regeneration) code is a set of n nodes used to store a file. For a file of total size kα, each node stores α symbols, any k nodes determine the file, and any d nodes can repair any other node by each sending out α/ (d- k+ 1) symbols. In this work, we express the product-matrix construction of (n, k, 2 (k- 1) , k- 1) -MSR codes in terms of symmetric algebras. We then generalize the product-matrix construction to (n,k,(k-1)tt-1,(k-1t-1))-MSR codes for general t⩾ 2 , while the t= 2 case recovers the product-matrix construction. Our codes’ sub-packetization level—α—is small and independent of n. It is less than L2.8(d-k+1), where L is Alrabiah–Guruswami’s lower bound on α. Furthermore, it is less than other MSR codes’ α for a set of practical parameters. Finally, we discuss how our code repairs multiple failures at once.

AB - An (n, k, d, α) -MSR (minimum storage regeneration) code is a set of n nodes used to store a file. For a file of total size kα, each node stores α symbols, any k nodes determine the file, and any d nodes can repair any other node by each sending out α/ (d- k+ 1) symbols. In this work, we express the product-matrix construction of (n, k, 2 (k- 1) , k- 1) -MSR codes in terms of symmetric algebras. We then generalize the product-matrix construction to (n,k,(k-1)tt-1,(k-1t-1))-MSR codes for general t⩾ 2 , while the t= 2 case recovers the product-matrix construction. Our codes’ sub-packetization level—α—is small and independent of n. It is less than L2.8(d-k+1), where L is Alrabiah–Guruswami’s lower bound on α. Furthermore, it is less than other MSR codes’ α for a set of practical parameters. Finally, we discuss how our code repairs multiple failures at once.

KW - Distributed storage system

KW - Minimum storage regeneration

KW - Multilinear algebra

KW - Regenerating code

UR - http://www.scopus.com/inward/record.url?scp=85116278763&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85116278763&partnerID=8YFLogxK

U2 - 10.1007/s00200-021-00526-3

DO - 10.1007/s00200-021-00526-3

M3 - Article

AN - SCOPUS:85116278763

JO - Applicable Algebra in Engineering, Communications and Computing

JF - Applicable Algebra in Engineering, Communications and Computing

SN - 0938-1279

ER -