Explicit Code Constructions for Distributed Storage Minimizing Repair Bandwidth

Regenerating codes are a class of recently developed codes for distributed storage, that permit data recovery from any k of n nodes, and also have the capability of repairing a failed node by connecting to any d nodes and downloading an amount of data, termed the repair bandwidth, that is on average, significantly less than the size of the data file. These codes optimally trade the storage space with the repair bandwidth, and the resulting tradeoff is termed ‘storage-repair bandwidth tradeoff’. While the existence of regenerating codes has been proven, no general explicit constructions were available prior to this work. The main focus of our work is on obtaining explicit constructions for regenerating codes. The second part of our work answers an open problem in the area of regenerating codes related to the achievability of the tradeoff under the additional constraint of replacing a failed node by its exact replica. A new framework for regenerating codes is introduced which provides a great deal of flexibility compared to the original setup, and can potentially decrease the data recovery time by a considerable amount.