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

Locality and Availability in Distributed Storage

This paper studies the problem of code symbol availability: a code symbol is said to have $(r, t)$-availability if it can be reconstructed from $t$ disjoint groups of other symbols, each of size at most $r$. For example, $3$-replication supports $(1, 2)$-availability as each symbol can be read from its $t= 2$ other (disjoint) replicas, i.e., $r=1$. However, the rate of replication must vanish like $\frac{1}{t+1}$ as the availability increases. This paper shows that it is possible to construct codes that can support a scaling number of parallel reads while keeping the rate to be an arbitrarily high constant. It further shows that this is possible with the minimum distance arbitrarily close to the Singleton bound. This paper also presents a bound demonstrating a trade-off between minimum distance, availability and locality. Our codes match the aforementioned bound and their construction relies on combinatorial objects called resolvable designs. From a practical standpoint, our codes seem useful for distributed storage applications involving hot data, i.e., the information which is frequently accessed by multiple processes in parallel.Comment: Submitted to ISIT 201

Replication based storage systems with local repair

We consider the design of regenerating codes for distributed storage systems that enjoy the property of local, exact and uncoded repair, i.e., (a) upon failure, a node can be regenerated by simply downloading packets from the surviving nodes and (b) the number of surviving nodes contacted is strictly smaller than the number of nodes that need to be contacted for reconstructing the stored file. Our codes consist of an outer MDS code and an inner fractional repetition code that specifies the placement of the encoded symbols on the storage nodes. For our class of codes, we identify the tradeoff between the local repair property and the minimum distance. We present codes based on graphs of high girth, affine resolvable designs and projective planes that meet the minimum distance bound for specific choices of file sizes

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