Maximum Distance Separable Array Codes Allowing Partial Collaboration

This letter considers the problem of repairing multiple node failures through partial collaboration in a distributed storage system (DSS). In the repair process, each failed node firstly connects to <inline-formula> <tex-math notation="LaTeX">$d\geq k$ </tex-math></inline-formula> alive nodes to download data, and then exchanges data with other repairing nodes. Partial collaboration allows each failed node to only connect to some (not all) of the other repairing nodes to exchange data. Constructions of partially collaborative regenerating codes with <inline-formula> <tex-math notation="LaTeX">$d=k$ </tex-math></inline-formula> at the minimum-storage regime have been studied before.We propose a code construction using the maximum distance separable (MDS) array codes to achieve <inline-formula> <tex-math notation="LaTeX">$d>k$ </tex-math></inline-formula>, and show that the constructed code asymptotically approaches the minimum storage repair point as the number of failed nodes grows.