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arXiv · 1004.4663

On the Existence of Optimal Exact-Repair MDS Codes for Distributed Storage

Changho Suh·Kannan Ramchandran
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Abstract

The high repair cost of (n,k) Maximum Distance Separable (MDS) erasure codes has recently motivated a new class of codes, called Regenerating Codes, that optimally trade off storage cost for repair bandwidth. In this paper, we address bandwidth-optimal (n,k,d) Exact-Repair MDS codes, which allow for any failed node to be repaired exactly with access to arbitrary d survivor nodes, where k<=d<=n-1. We show the existence of Exact-Repair MDS codes that achieve minimum repair bandwidth (matching the cutset lower bound) for arbitrary admissible (n,k,d), i.e., k<n and k<=d<=n-1. Our approach is based on interference alignment techniques and uses vector linear codes which allow to split symbols into arbitrarily small subsymbols.

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Changho Suh, Kannan Ramchandran. 2010-04-26. On the Existence of Optimal Exact-Repair MDS Codes for Distributed Storage. https://arxiv.org/abs/1004.4663

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