1,261 research outputs found
Private Information Retrieval Schemes With Product-Matrix MBR Codes
A private information retrieval (PIR) scheme allows a user to retrieve a file from a database without revealing any information on the file being requested. As of now, PIR schemes have been proposed for several kinds of storage systems, including replicated and MDS-coded systems. However, the problem of constructing PIR schemes on regenerating codes has been sparsely considered. A regenerating code is a storage code whose codewords are distributed among nodes, enabling efficient storage of files, as well as low-bandwidth retrieval of files and repair of nodes. Minimum-bandwidth regenerating (MBR) codes define a family of regenerating codes allowing a node repair with optimal bandwidth. Rashmi, Shah, and Kumar obtained a large family of MBR codes using the product-matrix (PM) construction. In this work, a new PIR scheme over PM-MBR codes is designed. The inherent redundancy of the PM structure is used to reduce the download communication complexity of the scheme. A lower bound on the PIR capacity of MBR-coded PIR schemes is derived, showing an interesting storage space vs. PIR rate trade-off compared to existing PIR schemes with the same reconstruction capability. The present scheme also outperforms a recent PM-MBR PIR construction of Dorkson and Ng.Peer reviewe
Bounds and Constructions for Generalized Batch Codes
Private information retrieval (PIR) codes and batch codes are two important
types of codes that are designed for coded distributed storage systems and
private information retrieval protocols. These codes have been the focus of
much attention in recent years, as they enable efficient and secure storage and
retrieval of data in distributed systems.
In this paper, we introduce a new class of codes called \emph{-batch
codes}. These codes are a type of storage codes that can handle any multi-set
of requests, comprised of distinct information symbols. Importantly,
PIR codes and batch codes are special cases of -batch codes.
The main goal of this paper is to explore the relationship between the number
of redundancy symbols and the -batch code property. Specifically, we
establish a lower bound on the number of redundancy symbols required and
present several constructions of -batch codes. Furthermore, we extend
this property to the case where each request is a linear combination of
information symbols, which we refer to as \emph{functional -batch
codes}. Specifically, we demonstrate that simplex codes are asymptotically
optimal functional -batch codes, in terms of the number of redundancy
symbols required, under certain parameter regime.Comment: 25 page
Constructions of Batch Codes via Finite Geometry
A primitive -batch code encodes a string of length into string
of length , such that each multiset of symbols from has mutually
disjoint recovering sets from . We develop new explicit and random coding
constructions of linear primitive batch codes based on finite geometry. In some
parameter regimes, our proposed codes have lower redundancy than previously
known batch codes.Comment: 7 pages, 1 figure, 1 tabl
Lifted Multiplicity Codes and the Disjoint Repair Group Property
Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We consider a generalization of their construction, which we call lifted multiplicity codes. These are multivariate polynomial codes whose restriction to any line is a codeword of a multiplicity code (Kopparty, Saraf, Yekhanin 2014). We show that lifted multiplicity codes have a better trade-off between redundancy and a notion of locality called the t-disjoint-repair-group property than previously known constructions. More precisely, we show that, for t <=sqrt{N}, lifted multiplicity codes with length N and redundancy O(t^{0.585} sqrt{N}) have the property that any symbol of a codeword can be reconstructed in t different ways, each using a disjoint subset of the other coordinates. This gives the best known trade-off for this problem for any super-constant t < sqrt{N}. We also give an alternative analysis of lifted Reed Solomon codes using dual codes, which may be of independent interest
Lengthening and Extending Binary Private Information Retrieval Codes
It was recently shown by Fazeli et al. that the storage overhead of a
traditional -server private information retrieval (PIR) protocol can be
significantly reduced using the concept of a -server PIR code. In this work,
we show that a family of -server PIR codes (with increasing dimensions and
blocklengths) can be constructed from an existing -server PIR code through
lengthening by a single information symbol and code extension by at most
code symbols. Furthermore, by extending a code
construction notion from Steiner systems by Fazeli et al., we obtain a specific
family of -server PIR codes. Based on a code construction technique that
lengthens and extends a -server PIR code simultaneously, a basic algorithm
to find good (i.e., small blocklength) -server PIR codes is proposed. For
the special case of , we find provably optimal PIR codes for code
dimensions , while for all we find codes of smaller
blocklength than the best known codes from the literature. Furthermore, in the
case of , we also find better codes for . Numerical
results show that most of the best found -server PIR codes can be
constructed from the proposed family of codes connected to Steiner systems.Comment: The shorter version of this paper will appear in the proceedings of
2018 International Zurich Seminar on Information and Communicatio
A Storage-Efficient and Robust Private Information Retrieval Scheme Allowing Few Servers
Since the concept of locally decodable codes was introduced by Katz and
Trevisan in 2000, it is well-known that information the-oretically secure
private information retrieval schemes can be built using locally decodable
codes. In this paper, we construct a Byzantine ro-bust PIR scheme using the
multiplicity codes introduced by Kopparty et al. Our main contributions are on
the one hand to avoid full replica-tion of the database on each server; this
significantly reduces the global redundancy. On the other hand, to have a much
lower locality in the PIR context than in the LDC context. This shows that
there exists two different notions: LDC-locality and PIR-locality. This is made
possible by exploiting geometric properties of multiplicity codes
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