A Network Coding Based Framework for Construction of Systematic Minimum Bandwidth Regenerating (MBR) Codes for Distributed Storage

Regenerating codes are a family of erasure correcting codes that are primarily designed to minimize the amount of data required to be downloaded to repair a failed node in a distributed storage system. In this article, the construction of systematic Minimum Bandwidth Regenerating (MBR) codes based on random network coding, is presented. The repair model considered is the hybrid repair model, wherein, the source (message) symbols are exactly replicated, while the redundant (parity) symbols are replaced by their functionally equivalent symbols. It is showed that the random network coding based constructions can preserve the practically favorable systematic feature and still achieve the optimal trade off between storage and repair bandwidth, if the coding is performed by combining the judiciously selected source symbols. Unlike most of the schemes present in the literature, the proposed constructions do not pose any restriction on the number of nodes participating in repair or on the total number of nodes, and thus add reconfigurability to the system. Moreover, during the repair of systematic nodes, the proposed codes require less number of disk reads compared to most of the codes in the literature. In the second half of the article, it is proven that the proposed constructions satisfy the necessary subspace properties of a linear exact regenerating code that are established in the literature. Further, rigorous analytical study of the effect of Galois field size on the probability of successful regeneration and reconstruction is carried out, and the results are validated using the numerical simulations.