Fractional repetition (FR) codes are a class of regenerating codes for distributed storage system... more 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 our work, we present 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. We also present local FR codes where the repair degree is smaller than the number of nodes contacted for reconstructing the stored file. For these codes a tradeoff between the local repair property and failure resilience is established and codes that meet this tradeoff are constructed. Much of prior work only provided lower bounds on the FR code rate. In our work, for most of our constructions we determine the code rate for certain parameter ranges.
2013 Asilomar Conference on Signals, Systems and Computers, 2013
ABSTRACT We consider the design of regenerating codes for distributed storage systems at the mini... more ABSTRACT 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.
In this paper, we show how certain three-class association schemes and orthogonal arrays give ris... more In this paper, we show how certain three-class association schemes and orthogonal arrays give rise to partial geometric designs. We also investigate the connections between partial geometric designs and certain regular graphs having three or four distinct eigenvalues, three-class association schemes, orthogonal arrays of strength two and particular linear codes. We give various characterizations of these graphs, association schemes and orthogonal arrays in terms of partial geometric designs. We also give a list of infinite families of directed strongly regular graphs arising from the partial geometric designs obtained in this paper.
We consider the design of regenerating codes for distributed storage systems at the minimum bandw... more 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.
We consider the design of regenerating codes for distributed storage systems that enjoy the prope... more 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.
Fractional repetition (FR) codes are a class of regenerating codes for distributed storage system... more 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 our work, we present 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. We also present local FR codes where the repair degree is smaller than the number of nodes contacted for reconstructing the stored file. For these codes a tradeoff between the local repair property and failure resilience is established and codes that meet this tradeoff are constructed. Much of prior work only provided lower bounds on the FR code rate. In our work, for most of our constructions we determine the code rate for certain parameter ranges.
2013 Asilomar Conference on Signals, Systems and Computers, 2013
ABSTRACT We consider the design of regenerating codes for distributed storage systems at the mini... more ABSTRACT 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.
In this paper, we show how certain three-class association schemes and orthogonal arrays give ris... more In this paper, we show how certain three-class association schemes and orthogonal arrays give rise to partial geometric designs. We also investigate the connections between partial geometric designs and certain regular graphs having three or four distinct eigenvalues, three-class association schemes, orthogonal arrays of strength two and particular linear codes. We give various characterizations of these graphs, association schemes and orthogonal arrays in terms of partial geometric designs. We also give a list of infinite families of directed strongly regular graphs arising from the partial geometric designs obtained in this paper.
We consider the design of regenerating codes for distributed storage systems at the minimum bandw... more 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.
We consider the design of regenerating codes for distributed storage systems that enjoy the prope... more 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.
Uploads
Papers by Oktay Olmez