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Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage (0906.4913v2)

Published 26 Jun 2009 in cs.IT and math.IT

Abstract: Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A subspace based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.

Citations (277)

Summary

  • The paper introduces explicit constructions of exact regenerating codes that enable precise node reconstruction at both the MBR and MSR points.
  • It employs a subspace-based approach and graph incidence matrices to minimize communication overhead and ensure efficient data recovery.
  • The constructions require minimal field size and low computational complexity, making them practical for scalable distributed storage systems.

Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

In the pursuit of enhancing distributed storage systems' reliability without incurring excessive storage overhead, the paper "Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage" by Rashmi, Shah, Kumar, and Ramchandran, contributes significantly by introducing and constructing explicit Exact Regenerating Codes, particularly for the minimum bandwidth and minimum storage points of the tradeoff curve established by Wu et al. The results demonstrate that such codes necessitate minimal processing and communication overhead, thereby bolstering system practicality and facilitating maintenance.

The paper's primary achievement lies in the development of Exact Regenerating Codes, which ensure that a failed node can be precisely reconstructed. This characteristic is particularly valuable, as it eliminates the need for system-wide updates post-regeneration, a cumbersome requirement when using conventional regenerating codes. The work meticulously explicates the construction of such exact codes at the minimum bandwidth regeneration (MBR) point, making them highly relevant to environments such as distributed mail servers, where expedited recovery from failures is paramount.

The authors adopt a subspace-based approach, which not only furnishes the necessary and sufficient conditions for linear codes to exhibit exact regeneration but also underpins the uniqueness of the derived construction. The theoretical framework is reinforced by explicit examples, where nodes are viewed as storing subspaces of a linear code, thus providing a comprehensive subspace perspective that supports effective data reconstruction and node regeneration.

At the MBR point, the explicit construction proposed involves nodes storing symbols from a fully connected graph's incidence matrix. Consequently, each node intersects uniquely with every other node, facilitating efficient and exact regeneration. The paper extensively discusses the implications of such structures, demonstrating that these codes minimize the regeneration bandwidth, thereby optimizing recovery time.

Towards practical implementation, the field size requisites for the proposed construction are minimal compared to network-coding-based solutions, thereby reducing computational complexity significantly. The use of Reed-Solomon codes ensures that the field size remains feasible, making real-world deployments plausible.

Moreover, the paper addresses the construction of regenerating codes at the minimum storage regeneration (MSR) point, intending to support peer-to-peer systems with limited node storage capabilities. These constructions are robust against multiple simultaneous node failures, thus offering a scalable and dynamic solution to distributed storage settings with fluctuating node availability.

The novel construction methods in the context of both MBR and MSR points not only highlight low complexity and field size requirements but also set a foundation for future enhancements in distributed storage systems. The implications of ensuring minimal overhead and robust system maintenance are profound, especially considering the evolving demands of data-centric environments.

In conclusion, this paper presents indispensable advancements in the design of exact regenerating codes, offering both theoretical clarity and practical executions that promise to enhance reliability and efficiency in distributed storage systems. Looking ahead, these contributions may spur further research into extending the applicability of exact regenerating codes across varying network architectures and storage constraints, thus potentially influencing AI deployment patterns across distributed infrastructures.