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 constructed array codes that achieve the optimal rebuilding ratio of 1/r 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 for an arbitrary erasure 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.
The work was subsequently extended in REF to include repair of the parity nodes.
On codes for optimal rebuilding access
2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Mathematics Computer Science