Error-Correcting Regenerating and Locally Repairable Codes via Rank-Metric Codes

Abstract: This paper presents and analyzes a novel concatenated coding scheme for enabling error resilience in two distributed storage settings: one being storage using existing regenerating codes and the second being storage using locally repairable codes. The concatenated coding scheme brings together a maximum rank distance (MRD) code as an outer code and either a globally regenerating or a locally repairable code as an inner code. Also, error resilience for combination of locally repairable codes with regenerating codes is considered. This concatenated coding system is designed to handle two different types of adversarial errors: the first type includes an adversary that can replace the content of an affected node only once; while the second type studies an adversary that is capable of polluting data an unbounded number of times. The paper establishes an upper bound on the resilience capacity for a locally repairable code and proves that this concatenated coding coding scheme attains the upper bound on resilience capacity for the first type of adversary. Further, the paper presents mechanisms that combine the presented concatenated coding scheme with subspace signatures to achieve error resilience for the second type of errors.