Fractional Repetition Codes Based on Partially Ordered Sets

Fractional repetition (FR) codes is a class of codes which were recently introduced for distributed storage systems. These codes are intended for exact uncoded repair of node failures, by downloading symbols from a suitable subset of surviving nodes. The repair procedure in FR codes is table based, unlike the regenerating codes, where the repair of a failed node is possible using arbitrary subset of a given size from surviving nodes. The advantage of this relaxation is that it allows to achieve low complexity in repair process, while these codes have minimum repair bandwidth like minimum bandwidth regenerating (MBR) codes. In this paper we give new and simple constructions for universally good FR codes based on partially ordered sets. These codes allow for efficient uncoded repair and the resulting designs are scalable and easy to implement. In particular, they allow to store larger files as compared to MBR codes. Furthermore, the constructions can be extended to FR codes for heterogeneous storage systems.