Multilinear Algebra for Distributed Storage

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.

33 pages, 6 figures, 1 table

References in corpus (6)

• Optimal Exact-Regenerating Codes for Distributed Storage at the MSR and MBR Points via a Product-Matrix Construction
• Outer bounds for exact repair codes
• Cascade Codes For Distributed Storage Systems
• A Note on the Rate Region of Exact-Repair Regenerating Codes
• Determinant Codes with Helper-Independent Repair for Single and Multiple Failures
• Enabling optimal access and error correction for the repair of Reed-Solomon codes

Cited by in corpus (1)

• Multilinear Algebra for Minimum Storage Regenerating Codes