Oktay Olmez

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 β ≥ 1 packets from a subset of the surviving nodes (prior work only considered the case of β = 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.

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.

Fractional Repetition Codes With Flexible Repair From Combinatorial Designs

Fractional repetition (FR) codes are a class of regenerating codes for distributed storage systems with an exact (table-based) repair process that is also uncoded, i.e., upon failure, a node is regenerated by simply downloading packets from the surviving nodes. In this paper, we present the constructions of FR codes based on Steiner systems and resolvable combinatorial designs, such as affine geometries, Hadamard designs, and mutually orthogonal Latin squares. The failure resilience of our codes can be varied in a simple manner. We construct codes with normalized repair bandwidth (β) strictly larger than one; these cannot be obtained trivially from codes with β = 1. Furthermore, we present the Kronecker product technique for generating new codes from existing ones and elaborate on their properties. FR codes with locality are those where the repair degree is smaller than the number of nodes contacted for reconstructing the stored file. For these codes, we establish a tradeoff between the local repair property and the failure resilience and construct codes that meet this tradeoff. Much of prior work only provided lower bounds on the FR code rate. In this paper, for most of our constructions, we determine the code rate for certain parameter ranges.

Some Families of Directed Strongly Regular Graphs Obtained from Certain Finite Incidence Structures

We present many new directed strongly regular graphs by direct construction. We construct these graphs on the collections of antiflags of certain finite incidence structures. In this way, we confirm the feasibility of infinitely many parameter sets that was previously undetermined. We describe some examples of graphs together with their isomorphism classes to demonstrate the fact that our construction method is capable of producing many graphs with same parameters.

Constructions of fractional repetition codes from combinatorial designs

We consider the design of regenerating codes for distributed storage systems at the minimum bandwidth regeneration (MBR) point. Our codes consist of an outer MDS code followed by an inner fractional repetition (FR) code (introduced in prior work). In these systems a failed node can be repaired by simply downloading packets from surviving nodes. We present constructions that use the Kronecker product to construct new fractional repetition codes from existing codes. We demonstrate that an infinite family of codes can be generated by considering the Kronecker product of two Steiner systems that have the same storage capacity. The resultant code inherits its normalized repair bandwidth from the storage capacity of the original Steiner systems and has the maximum level of failure resilience possible. We also present some properties of the Kronecker product of resolvable designs and the corresponding file sizes.

Plateaued functions and one-and-half difference sets

We construct an infinite family of

Partial geometric designs with prescribed automorphisms

1\frac{1}{2}

Symmetric 112-Designs and 112-Difference Sets

112-difference sets in non-cyclic abelian