Exact Regenerating Codes for Distributed Storage

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Abstract
Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. The bandwidth required to repair the system after a node failure also plays a crucial role in the system performance. In [1] authors have shown that a tradeoff exists between storage and repair bandwidth. They also have introduced the scheme of regenerating codes which meet this tradeoff. In this paper, a scheme of Exact Regenerating Codes is introduced, which are regenerating codes with an additional property of regenerating back the same node upon failure. For the minimum bandwidth point, which is suitable for applications like distributed mail servers, explicit construction for exact regenerating codes is provided. A subspace approach is provided, using which the necessary and sufficient conditions for a linear code to be an exact regenerating code are derived. This leads to the uniqueness of our construction. For the minimum storage point which suits applications such as storage in peer-to-peer systems, an explicit construction of regenerating codes for certain suitable parameters is provided. This code supports variable number of nodes and can handle multiple simultaneous node failures. The constructions given for both the points require a low field size and have low complexity.

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