Update-Efficient Regenerating Codes with Minimum Per-Node Storage

Regenerating codes provide an efficient way to recover data at failed nodes in distributed storage systems. It has been shown that regenerating codes can be designed to minimize the per-node storage (called MSR) or minimize the communication overhead for regeneration (called MBR). In this work, we propose a new encoding scheme for [n,d] error- correcting MSR codes that generalizes our earlier work on error-correcting regenerating codes. We show that by choosing a suitable diagonal matrix, any generator matrix of the [n,{\alpha}] Reed-Solomon (RS) code can be integrated into the encoding matrix. Hence, MSR codes with the least update complexity can be found. An efficient decoding scheme is also proposed that utilizes the [n,{\alpha}] RS code to perform data reconstruction. The proposed decoding scheme has better error correction capability and incurs the least number of node accesses when errors are present.Comment: Submitted to IEEE ISIT 201

Error Resilience in Distributed Storage via Rank-Metric Codes

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