Update Bandwidth for Distributed Storage

In this paper, we consider the update bandwidth in distributed storage systems (DSSs). The bandwidth, which measures transmission efficiency of process DSSs, is defined as average amount data symbols transferred network when stored a node are updated. This paper contains following contributions. First, establish closed-form expression minimum attainable by irregular array codes. Second, after defining class codes, called Minimum Update Bandwidth (MUB) achieve determine smallest code redundancy MUB Third, parameters, with codes and can be equal, identified, allows us to define MR-MUB that simultaneously bandwidth. Fourth, introduce explicit constructions redundancy. Fifth, lower bound complexity used prove may not achieved Last, construct $(n = k + 2, k)$ vertical maximum-distance separable (MDS) all redundancy, optimal repair