Codes with Local Regeneration
  Regenerating codes and codes with locality are two schemes that have recently been proposed to ensure data collection and reliability in a distributed storage network. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. In this paper, we provide several constructions for a class of vector codes with locality in which the local codes are regenerating codes, that enjoy both advantages. We derive an upper bound on the minimum distance of this class of codes and show that the proposed constructions achieve this bound. The constructions include both the cases where the local regenerating codes correspond to the MSR as well as the MBR point on the storage-repair-bandwidth tradeoff curve of regenerating codes. Also included is a performance comparison of various code constructions for fixed block length and minimum distance. 
Govinda M. Kamath, N. Prakash, V. Lalitha and P. Vijay Kumar
cs.IT math.IT