HFR Code: A Flexible Replication Scheme for Cloud Storage Systems

Fractional repetition (FR) codes are a family of repair-efficient storage codes that provide exact and uncoded node repair at the minimum bandwidth regenerating point. The advantageous repair properties are achieved by a tailor-made two-layer encoding scheme which concatenates an outer maximum-distance-separable (MDS) code and an inner repetition code. In this paper, we generalize the application of FR codes and propose heterogeneous fractional repetition (HFR) code, which is adaptable to the scenario where the repetition degrees of coded packets are different. We provide explicit code constructions by utilizing group divisible designs, which allow the design of HFR codes over a large range of parameters. The constructed codes achieve the system storage capacity under random access repair and have multiple repair alternatives for node failures. Further, we take advantage of the systematic feature of MDS codes and present a novel design framework of HFR codes, in which storage nodes can be wisely partitioned into clusters such that data reconstruction time can be reduced when contacting nodes in the same cluster.Comment: Accepted for publication in IET Communications, Jul. 201

Load-Balanced Fractional Repetition Codes

We introduce load-balanced fractional repetition (LBFR) codes, which are a strengthening of fractional repetition (FR) codes. LBFR codes have the additional property that multiple node failures can be sequentially repaired by downloading no more than one block from any other node. This allows for better use of the network, and can additionally reduce the number of disk reads necessary to repair multiple nodes. We characterize LBFR codes in terms of their adjacency graphs, and use this characterization to present explicit constructions LBFR codes with storage capacity comparable existing FR codes. Surprisingly, in some parameter regimes, our constructions of LBFR codes match the parameters of the best constructions of FR codes

Repairable Replication-based Storage Systems Using Resolvable Designs

We consider the design of regenerating codes for distributed storage systems at the minimum bandwidth regeneration (MBR) point. The codes allow for a repair process that is exact and uncoded, but table-based. These codes were introduced in prior work and consist of an outer MDS code followed by an inner fractional repetition (FR) code where copies of the coded symbols are placed on the storage nodes. The main challenge in this domain is the design of the inner FR code. In our work, we consider generalizations of FR codes, by establishing their connection with a family of combinatorial structures known as resolvable designs. Our constructions based on affine geometries, Hadamard designs and mutually orthogonal Latin squares allow the design of systems where a new node can be exactly regenerated by downloading $\beta \geq 1$ packets from a subset of the surviving nodes (prior work only considered the case of $\beta = 1$). Our techniques allow the design of systems over a large range of parameters. Specifically, the repetition degree of a symbol, which dictates the resilience of the system can be varied over a large range in a simple manner. Moreover, the actual table needed for the repair can also be implemented in a rather straightforward way. Furthermore, we answer an open question posed in prior work by demonstrating the existence of codes with parameters that are not covered by Steiner systems