A subspace regenerating code with minimum decoding bandwidth

Abstract

Hollmann built a theoretical framework for subspace regenerating storage code. In this framework, a storage node is equipped with a constant dimension subspace chosen from an overall message space F m q . The projection of user message on the subspace is stored on the corresponding node. A subspace code needs to fulfil decoding and repairing functionality. The framework stipulates the property for subspace storage code, but a simple implementable construction is still missing. To decrease the complexity of code design as well as encoding and decoding, this article proposed a subspace code implementation over F 2 with the parameters of (m, m, 2, ⌈ m 2 ⌉, r, 𝜷). It is proved theoretically the code is characterized by minimum decoding bandwidth, minimum storage, and exact repair. Still, the code is explicit, feasible and lightweight. A series of examples are given to elucidate the encoding, decoding and repairing procedures, which show in cases of m ≤ 5, the code could achieve high repair efficiency by combining with network coding.