Distributed storage systems based on intersecting subspace codes

Raviv, Netanel; Etzion, Tuvi

doi:10.1109/isit.2015.7282698

Cited by 14 publications

(21 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In what follows we will translate the vectorspace definitions of [8, Definitions 3.1, 3.2] into the language of projective spaces. We will see that this provides new insight into existing constructions of repair codes, such as [8,17], as well as suggesting useful frameworks for new construction of such codes. Definition 2.1 ((r, β)-repair).…”

Section: (Ii) (Repair)mentioning

confidence: 87%

“…This is due to the fact that the elements stored by a node allow them to recover any desired element in the corresponding space, and this ability does not depend on the choice of basis used to describe the space. We note that in [17], the term functional repair is used in a scenario in which the failed node and the repaired node correspond to different bases of the same space. However, this would satisfy Defintion 2.4 for exact repair, and hence would not represent a strictly functional repair code according to our usage of terminology in this paper.…”

Section: (B) (Repair)mentioning

confidence: 99%

“…In this environment where greater flexibility is possible, this implies that the spaces must be chosen carefully to achieve the desired intersection properties. Here we consider an example of a construction from [17]. It uses subspace codes constructed from Grassmann varieties in vector spaces.…”

Section: Grassmann Varietiesmentioning

confidence: 99%

See 2 more Smart Citations

Functional repair codes: a view from projective geometry

Paterson

2019

Des. Codes Cryptogr.

View full text Add to dashboard Cite

Storage codes are used to ensure reliable storage of data in distributed systems. Here we consider functional repair codes, where individual storage nodes that fail may be repaired efficiently and the ability to recover original data and to further repair failed nodes is preserved. There are two predominant approaches to repair codes: a coding theoretic approach and a vector space approach. We explore the relationship between the two and frame the later in terms of projective geometry. We find that many of the constructions proposed in the literature can be seen to arise from natural and well-studied geometric objects, and that this perspective gives a framework that provides opportunities for generalisations and new constructions that can lead to greater flexibility in trade-offs between various desirable properties. We also frame the cut-set bound obtained from network coding in terms of projective geometry.We explore the notion of strictly functional repair codes, for which there exist nodes that cannot be replaced exactly. Currently only one known example is given in the literature, due to Hollmann and Poh. We examine this phenomenon from a projective geometry point of view, and discuss how strict functionality can arise.Finally, we consider the issue that the view of a repair code as a collection of sets of vector/projective subspaces is recursive in nature and makes it hard to visualise what a collection of nodes looks like and how one might approach a construction. Here we provide another view of using directed graphs that gives us non-recursive criteria for determining whether a family of collections of subspaces constitutes a function, exact, or strictly functional repair code, which may be of use in searching for new codes with desirable properties.

show abstract

Section: (Ii) (Repair)mentioning

confidence: 87%

Section: (B) (Repair)mentioning

confidence: 99%

See 1 more Smart Citation

Functional repair codes: a view from projective geometry

Paterson

2019

Des. Codes Cryptogr.

View full text Add to dashboard Cite

show abstract

“…Further aspects of regenerating codes where thoroughly studied in recent years [2,7,8,9,18,21,26]. In particular, the problem of constructing high rate MSR codes, i.e., with a constant number of parity nodes, has received a great deal of attention [4,22,24,29,30].…”

Section: Previous Workmentioning

confidence: 99%

Asymptotically Optimal Regenerating Codes Over Any Field

Raviv

2018

IEEE Trans. Inform. Theory

Self Cite

View full text Add to dashboard Cite

The study of regenerating codes has advanced tremendously in recent years. However, most known constructions require large field size, and hence may be hard to implement in practice. By using notions from the theory of extension fields, we obtain two explicit constructions of regenerating codes. These codes approach the cut-set bound as the reconstruction degree increases, and may be realized over any given field if the file size is large enough. Since distributed storage systems are the main purpose of regenerating codes, this file size restriction is trivially satisfied in most conceivable scenarios. The first construction attains the cut-set bound at the MBR point asymptotically for all parameters, whereas the second one attains the cut-set bound at the MSR point asymptotically for low-rate parameters.

show abstract

“…Equidistant subspace codes were shown to have relevant applications in distributed storage in [20]. In the same paper, Etzion and Raviv identify two trivial families of equidistant codes, namely sunflowers and balls.…”

Section: Introductionmentioning

confidence: 96%

Equidistant subspace codes

Gorla

Ravagnani

2016

Linear Algebra and its Applications

View full text Add to dashboard Cite

In this paper we study equidistant subspace codes, i.e. subspace codes with the property that each two distinct codewords have the same distance. We provide an almost complete classification of such codes under the assumption that the cardinality of the ground field is large enough. More precisely, we prove that for most values of the parameters, an equidistant code of maximum cardinality is either a sunflower or the orthogonal of a sunflower. We also study equidistant codes with extremal parameters, and establish general properties of equidistant codes that are not sunflowers. Finally, we propose a systematic construction of equidistant codes based on our previous construction of partial spread codes, and provide an efficient decoding algorithm.

show abstract

Distributed storage systems based on intersecting subspace codes

Cited by 14 publications

References 18 publications

Functional repair codes: a view from projective geometry

Functional repair codes: a view from projective geometry

Asymptotically Optimal Regenerating Codes Over Any Field

Equidistant subspace codes

Contact Info

Product

Resources

About