Scalable (n, k, d) exact-repair regenerating codes with small repair bandwidth

This paper focuses on the design of regeneration codes. An (n, k, d) exact-regenerating code encodes and stores the data into n nodes such that the entire data can be recovered from any k nodes, and the missing coded information of any failed node can be identically recovered by the help of d nodes. In an earlier work of the authors, determinant codes are introduced for any (n, k, d = k) system, and they are shown to achieve the optimum tradeoff between the node storage α and the repair-bandwidth β In this work, the latter constraint of d = k is relaxed, and the construction of determinant codes is generalized to arbitrary parameters (n, k, d), for a certain range of (α,β). The proposed construction is scalable, in the sense that the system performance only depend on k and d, and the same of operating point (α,β) can be universally achieved for any number of nodes n. The resulting codes are linear, and the required size of the underlying finite field is not greater than Θ(n).