The fundamental theorem of distributed storage systems revisited

The fundamental theorem of distributed storage systems characterizes the maximum file size that can be stored with certain assumptions on file retrieval and node repair. The result is composed of two parts, namely, the min-cut bound and that the bound can be achieved by linear network code with bounded field size. The derivation of the min-cut bound is reexamined and illuminated by making an implicit step explicit. Furthermore, a simple alternative proof for the achievability of the min-cut bound is presented, which is based on the construction of the generic storage code, a restricted form of generic network code. The proof techniques in this paper are expected to be extensible to other more complex models of distributed storage systems.