On Codes for Optimal Rebuilding Access

TL;DR

This paper introduces new array codes that achieve the optimal rebuilding ratio of 1/r for any single node in storage systems, significantly reducing data access during recovery.

Contribution

The paper constructs array codes that attain the theoretical lower bound of 1/r for rebuilding any single node, including parity nodes, solving a previously open problem.

Findings

Achieved the optimal rebuilding ratio of 1/r for all nodes.

Constructed array codes that match the lower bound for data access.

Reduced data access during node recovery in storage systems.

Abstract

MDS (maximum distance separable) array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with r redundancy nodes can correct any r erasures by accessing (reading) all the remaining information in both the systematic nodes and the parity (redundancy) nodes. However, in practice, a single erasure is the most likely failure event; hence, a natural question is how much information do we need to access in order to rebuild a single storage node? We define the rebuilding ratio as the fraction of remaining information accessed during the rebuilding of a single erasure. In our previous work we showed that the optimal rebuilding ratio of 1/r is achievable (using our newly constructed array codes) for the rebuilding of any systematic node, however, all the information needs to be accessed for the rebuilding of the parity nodes. Namely, constructing array codes with a rebuilding ratio of 1/r was left as an open problem. In this paper, we solve this open problem and present array codes that achieve the lower bound of 1/r for rebuilding any single systematic or parity node.