On Code Rates of Fractional Repetition Codes

In \textit{Distributed Storage Systems} (DSSs), usually, data is stored using replicated packets on different chunk servers. Recently a new paradigm of \textit{Fractional Repetition} (FR) codes have been introduced, in which, data is replicated in a smart way on distributed servers using a \textit{Maximum Distance Separable} (MDS) code. In this work, for a non-uniform FR code, bounds on the FR code rate and DSS code rate are studied. Using matrix representation of an FR code, some universally good FR codes have been obtained.Comment: 11 pages, 0 figure

Bounds on Fractional Repetition Codes using Hypergraphs

In the \textit{Distributed Storage Systems} (DSSs), an encoded fraction of information is stored in the distributed fashion on different chunk servers. Recently a new paradigm of \textit{Fractional Repetition} (FR) codes have been introduced, in which, encoded data information is stored on distributed servers, where encoding is done using a \textit{Maximum Distance Separable} (MDS) code and a smart replication of packets. In this work, we have shown that an FR code is equivalent to a hypergraph. Using the correspondence, the properties and the bounds of a hypergraph are directly mapped to the associated FR code. In general, the necessary and sufficient conditions for the existence of an FR code is obtained by using the correspondence. Some of the bounds are new and FR codes meeting these bounds are unknown. It is also shown that any FR code associated with a linear hypergraph is universally good.Comment: 8 pages, 2 figure

On the Duality and File Size Hierarchy of Fractional Repetition Codes

Distributed storage systems that deploy erasure codes can provide better features such as lower storage overhead and higher data reliability. In this paper, we focus on fractional repetition (FR) codes, which are a class of storage codes characterized by the features of uncoded exact repair and minimum repair bandwidth. We study the duality of FR codes, and investigate the relationship between the supported file size of an FR code and its dual code. Based on the established relationship, we derive an improved dual bound on the supported file size of FR codes. We further show that FR codes constructed from $t$-designs are optimal when the size of the stored file is sufficiently large. Moreover, we present the tensor product technique for combining FR codes, and elaborate on the file size hierarchy of resulting codes.Comment: Submitted for possible journal publicatio

On Universally Good Flower Codes

For a Distributed Storage System (DSS), the \textit{Fractional Repetition} (FR) code is a class in which replicas of encoded data packets are stored on distributed chunk servers, where the encoding is done using the Maximum Distance Separable (MDS) code. The FR codes allow for exact uncoded repair with minimum repair bandwidth. In this paper, FR codes are constructed using finite binary sequences. The condition for universally good FR codes is calculated on such sequences. For some sequences, the universally good FR codes are explored.Comment: 18 pages, 2 Figures, submitted to SETA 201

On the Optimal Minimum Distance of Fractional Repetition Codes

Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the smallest number of nodes whose failure leads to the unrecoverable loss of the stored file. We consider upper bounds on the minimum distance and present several families of explicit FR codes attaining these bounds. The optimal constructions are derived from regular graphs and combinatorial designs, respectively