Error Resilience in Distributed Storage via Rank-Metric Codes

TL;DR

This paper introduces a new coding scheme for distributed storage systems that enhances error resilience against adversarial attacks, using concatenated rank-metric and MDS array codes, with proven capacity bounds and practical constructions.

Contribution

It proposes a concatenated coding scheme combining MRD and MDS array codes, achieving optimal resilience against different types of adversarial errors in distributed storage.

Findings

Achieves upper bound on resilience capacity for single-instance adversarial errors.

Combines codes with subspace signatures for unbounded error tolerance.

Provides a construction for optimal locally repairable scalar codes.

Abstract

This paper presents a novel coding scheme for distributed storage systems containing nodes with adversarial errors. The key challenge in such systems is the propagation of erroneous data from a single corrupted node to the rest of the system during a node repair process. This paper presents a concatenated coding scheme which is based on two types of codes: maximum rank distance (MRD) code as an outer code and optimal repair maximal distance separable (MDS) array code as an inner code. Given this, two different types of adversarial errors are considered: the first type considers an adversary that can replace the content of an affected node only once; while the second attack-type considers an adversary that can pollute data an unbounded number of times. This paper proves that the proposed coding scheme attains a suitable upper bound on resilience capacity for the first type of error. Further, the paper presents mechanisms that combine this code with subspace signatures to achieve error resilience for the second type of errors. Finally, the paper concludes by presenting a construction based on MRD codes for optimal locally repairable scalar codes that can tolerate adversarial errors.