Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

TL;DR

This paper presents explicit constructions of optimal exact regenerating codes for distributed storage, enabling efficient data repair with minimal bandwidth and storage overhead, suitable for practical systems like mail servers and peer-to-peer networks.

Contribution

It introduces explicit, low-complexity constructions of exact regenerating codes at key points on the tradeoff curve, with a subspace approach and proofs of uniqueness.

Findings

Constructed codes for minimum bandwidth point with low complexity.

Developed codes for minimum storage point supporting multiple failures.

Provided necessary and sufficient conditions for exact regeneration in linear codes.

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 recent 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.