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MDS (maximum distance separable) array codes are widely used in storagesystems due to their computationally efficient encoding and decodingprocedures. An MDS code with r redundancy nodes can correct any r erasures byaccessing (reading) all the remaining information in both the systematic nodesand the parity (redundancy) nodes. However, in practice, a single erasure isthe most likely failure event; hence, a natural question is how muchinformation do we need to access in order to rebuild a single storage node? Wedefine the rebuilding ratio as the fraction of remaining information accessedduring the rebuilding of a single erasure. In our previous work we showed thatthe optimal rebuilding ratio of 1/r is achievable (using our newly constructedarray codes) for the rebuilding of any systematic node, however, all theinformation 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 anopen problem. In this paper, we solve this open problem and present array codesthat achieve the lower bound of 1/r for rebuilding any single systematic orparity node.

On Codes for Optimal Rebuilding Access