Centralized Repair of Multiple Node Failures with Applications to Communication Efficient Secret Sharing

TL;DR

This paper explores a centralized multi-node repair model in distributed storage, deriving bandwidth-storage trade-offs, constructing codes for optimal repair points, and applying these to develop communication-efficient secret sharing schemes.

Contribution

It introduces a generalized centralized repair model, derives tight repair bandwidth bounds, and constructs codes for optimal repair points, extending applications to secret sharing.

Findings

Derived repair bandwidth bounds for MSMR and MBMR points.

Constructed codes achieving MSMR and MBMR points under various conditions.

Applied the repair model to design bandwidth-efficient secret sharing schemes.

Abstract

This paper considers a distributed storage system, where multiple storage nodes can be reconstructed simultaneously at a centralized location. This centralized multi-node repair (CMR) model is a generalization of regenerating codes that allow for bandwidth-efficient repair of a single failed node. This work focuses on the trade-off between the amount of data stored and repair bandwidth in this CMR model. In particular, repair bandwidth bounds are derived for the minimum storage multi-node repair (MSMR) and the minimum bandwidth multi-node repair (MBMR) operating points. The tightness of these bounds are analyzed via code constructions. The MSMR point is characterized through codes achieving this point under functional repair for general set of CMR parameters, as well as with codes enabling exact repair for certain CMR parameters. The MBMR point, on the other hand, is characterized with exact repair codes for all CMR parameters for systems that satisfy a certain entropy accumulation property. Finally, the model proposed here is utilized for the secret sharing problem, where the codes for the multi-node repair problem is used to construct communication efficient secret sharing schemes with the property of bandwidth efficient share repair.