Self-repairing Homomorphic Codes for Distributed Storage Systems (1008.0064v1)

Abstract: Erasure codes provide a storage efficient alternative to replication based redundancy in (networked) storage systems. They however entail high communication overhead for maintenance, when some of the encoded fragments are lost and need to be replenished. Such overheads arise from the fundamental need to recreate (or keep separately) first a copy of the whole object before any individual encoded fragment can be generated and replenished. There has been recently intense interest to explore alternatives, most prominent ones being regenerating codes (RGC) and hierarchical codes (HC). We propose as an alternative a new family of codes to improve the maintenance process, which we call self-repairing codes (SRC), with the following salient features: (a) encoded fragments can be repaired directly from other subsets of encoded fragments without having to reconstruct first the original data, ensuring that (b) a fragment is repaired from a fixed number of encoded fragments, the number depending only on how many encoded blocks are missing and independent of which specific blocks are missing. These properties allow for not only low communication overhead to recreate a missing fragment, but also independent reconstruction of different missing fragments in parallel, possibly in different parts of the network. We analyze the static resilience of SRCs with respect to traditional erasure codes, and observe that SRCs incur marginally larger storage overhead in order to achieve the aforementioned properties. The salient SRC properties naturally translate to low communication overheads for reconstruction of lost fragments, and allow reconstruction with lower latency by facilitating repairs in parallel. These desirable properties make self-repairing codes a good and practical candidate for networked distributed storage systems.

• The paper presents a novel method using self-repairing codes that repair lost fragments directly without the need for full data reconstruction.
• The paper demonstrates that SRCs reduce communication overhead by repairing missing data with only two fragments via simple XOR operations.
• The paper highlights a symmetric design that supports parallel, independent repairs, significantly accelerating system recovery in distributed storage.

Overview of Self-Repairing Homomorphic Codes for Distributed Storage Systems

This paper introduces and explores self-repairing codes (SRCs) as a novel approach to enhance data maintenance efficiency in distributed storage systems. Building on the established benefits of erasure codes for storage redundancy, the authors identify the significant communication overheads associated with traditional erasure code maintenance. The self-repairing codes aim to address these challenges by enabling direct repair of encoded fragments from other fragments without reconstructing the original data first.

Key Features of Self-Repairing Codes

The distinguishing properties of SRCs are:

1. Direct Fragment Repair: Unlike traditional erasure codes, SRCs allow for the direct repair of missing fragments. This approach eliminates the need to reconstruct the original data before replenishing lost fragments.
2. Independence of Specific Fragment Loss: The number of fragments required for repairing a missing fragment is determined by the count of missing fragments, not the specific identities of the missing fragments, allowing for symmetry in encoded fragment roles.
3. Parallel and Independent Repairs: SRCs support the independent reconstruction of different missing fragments, facilitating repairs to occur simultaneously and efficiently across distributed networks.

Comparison with Regenerating and Hierarchical Codes

SRCs present a solution within the same design space as regenerating codes (RGCs) and hierarchical codes (HCs), yet with key differences:

• RGCs: While RGCs leverage network coding to minimize maintenance overheads, they still necessitate communication with at least k nodes for any repair, resulting in potentially higher complexity and overheads.
• HCs: These codes lack the symmetric roles among fragments, often needing varying numbers of fragments depending on which specific fragments are missing for reconstruction, a limitation not present in SRCs.

Self-Repairing Codes Design and Analysis

The paper proposes self-repairing codes constructed using weakly linearized polynomials. Through the concept of Homomorphic Self-Repairing Codes (HSRC), the authors present a practical implementation that achieves:

• Low Communication Overhead: A missing fragment can typically be reconstructed by downloading only two other fragments, which significantly reduces communication overhead.
• Computational Efficiency: The self-repair operation involves simply XORing encoded blocks, minimizing computational demands.

The authors conduct a thorough static resilience analysis and show that while SRCs incur marginally larger storage overhead compared to traditional erasure codes, they offer enhanced maintenance efficiency. Additionally, SRCs enable faster system recovery from vulnerable states by optimizing repair latency and bandwidth use.

Implications and Future Directions

The introduction of SRCs offers substantial implications for distributed storage systems:

• Reduced Bandwidth and Latency: SRCs potentially lower the bandwidth consumption during reconstruction processes and allow for expedited repair of lost redundancy.
• Flexible Deployment: By accommodating both eager and lazy repair strategies effectively, SRCs provide deployment flexibility in diverse network environments.
• Complexity Management: The construction of SRCs mitigates complexity via a symmetric structure, contrasting with the traditionally complex and resource-intensive regenerating codes.

Future research may explore further optimization of SRCS, including developing efficient decoding algorithms, strategizing encoded fragment placement concerning network topology, and fully leveraging SRCs' potential for parallel repairs. Such advances could solidify SRCs as a predominant methodology in the maintenance of distributed storage systems.