Codes Between MBR and MSR Points With Exact Repair Property

In this paper, distributed storage systems with exact repair are studied. Constructions for exact-regenerating codes between the minimum storage regenerating (MSR) and the minimum bandwidth regenerating (MBR) points are given. To the best of our knowledge, no previous construction of exact-regenerating codes between MBR and MSR points is done except in the works by Tian et al. and Sasidharan et al. In contrast to their works, the methods used here are elementary. In this paper, it is shown that in the case that the parameters \(n\) , \(k\) , and \(d\) are close to each other, the given construction is close to optimal when comparing with the known functional repair capacity. This is done by showing that when the distances of the parameters \(n\) , \(k\) , and \(d\) are fixed but the actual values approach to infinity, the fraction of the performance of constructed codes with exact repair and the known capacity of codes with functional repair, approaches to one. Also, a simple variation of the constructed codes with almost the same performance is given. Also some bounds for the capacity of exact-repairing codes are given. These bounds illustrate the relationships between storage codes with different parameters.