TL;DR
This paper develops a multilinear algebra framework to construct exact-repair regenerating codes for distributed storage, unifying and extending existing trade-offs and repair strategies.
Contribution
It introduces a multilinear algebra foundation for assembling ERRCs across all relevant parameters, linking trade-offs with cascade codes and addressing multiple failure repairs.
Findings
Established a multilinear algebra foundation for ERRCs.
Connected ERRCs with cascade code trade-offs.
Provided methods for repairing multiple failures.
Abstract
An -ERRC (exact-repair regenerating code) is a collection of nodes used to store a file. For a file of total size , each node stores symbols, any nodes recover the file, and any nodes repair any other node via sending out symbols. We establish a multilinear algebra foundation to assemble -ERRCs for all meaningful tuples. Our ERRCs tie the -versus- 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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