33,552 research outputs found
PIR Array Codes with Optimal Virtual Server Rate
There has been much recent interest in Private information Retrieval (PIR) in
models where a database is stored across several servers using coding
techniques from distributed storage, rather than being simply replicated. In
particular, a recent breakthrough result of Fazelli, Vardy and Yaakobi
introduces the notion of a PIR code and a PIR array code, and uses this notion
to produce efficient PIR protocols.
In this paper we are interested in designing PIR array codes. We consider the
case when we have servers, with each server storing a fraction of
the bits of the database; here is a fixed rational number with . A
PIR array code with the -PIR property enables a -server PIR protocol
(with ) to be emulated on servers, with the overall storage
requirements of the protocol being reduced. The communication complexity of a
PIR protocol reduces as grows, so the virtual server rate, defined to be
, is an important parameter. We study the maximum virtual server rate of a
PIR array code with the -PIR property. We present upper bounds on the
achievable virtual server rate, some constructions, and ideas how to obtain PIR
array codes with the highest possible virtual server rate. In particular, we
present constructions that asymptotically meet our upper bounds, and the exact
largest virtual server rate is obtained when .
A -PIR code (and similarly a -PIR array code) is also a locally
repairable code with symbol availability . Such a code ensures
parallel reads for each information symbol. So the virtual server rate is very
closely related to the symbol availability of the code when used as a locally
repairable code. The results of this paper are discussed also in this context,
where subspace codes also have an important role
An MDS-PIR Capacity-Achieving Protocol for Distributed Storage Using Non-MDS Linear Codes
We propose a private information retrieval (PIR) protocol for distributed
storage systems with noncolluding nodes where data is stored using an arbitrary
linear code. An expression for the PIR rate, i.e., the ratio of the amount of
retrieved data per unit of downloaded data, is derived, and a necessary and a
sufficient condition for codes to achieve the maximum distance separable (MDS)
PIR capacity are given. The necessary condition is based on the generalized
Hamming weights of the storage code, while the sufficient condition is based on
code automorphisms. We show that cyclic codes and Reed-Muller codes satisfy the
sufficient condition and are thus MDS-PIR capacity-achieving.Comment: To be presented at 2018 IEEE International Symposium on Information
Theory (ISIT). arXiv admin note: substantial text overlap with
arXiv:1712.0389
Achieving Maximum Distance Separable Private Information Retrieval Capacity With Linear Codes
We propose three private information retrieval (PIR) protocols for
distributed storage systems (DSSs) where data is stored using an arbitrary
linear code. The first two protocols, named Protocol 1 and Protocol 2, achieve
privacy for the scenario with noncolluding nodes. Protocol 1 requires a file
size that is exponential in the number of files in the system, while Protocol 2
requires a file size that is independent of the number of files and is hence
simpler. We prove that, for certain linear codes, Protocol 1 achieves the
maximum distance separable (MDS) PIR capacity, i.e., the maximum PIR rate (the
ratio of the amount of retrieved stored data per unit of downloaded data) for a
DSS that uses an MDS code to store any given (finite and infinite) number of
files, and Protocol 2 achieves the asymptotic MDS-PIR capacity (with infinitely
large number of files in the DSS). In particular, we provide a necessary and a
sufficient condition for a code to achieve the MDS-PIR capacity with Protocols
1 and 2 and prove that cyclic codes, Reed-Muller (RM) codes, and a class of
distance-optimal local reconstruction codes achieve both the finite MDS-PIR
capacity (i.e., with any given number of files) and the asymptotic MDS-PIR
capacity with Protocols 1 and 2, respectively. Furthermore, we present a third
protocol, Protocol 3, for the scenario with multiple colluding nodes, which can
be seen as an improvement of a protocol recently introduced by Freij-Hollanti
et al.. Similar to the noncolluding case, we provide a necessary and a
sufficient condition to achieve the maximum possible PIR rate of Protocol 3.
Moreover, we provide a particular class of codes that is suitable for this
protocol and show that RM codes achieve the maximum possible PIR rate for the
protocol. For all three protocols, we present an algorithm to optimize their
PIR rates.Comment: This work is the extension of the work done in arXiv:1612.07084v2.
The current version introduces further refinement to the manuscript. Current
version will appear in the IEEE Transactions on Information Theor
Asymmetry Helps: Improved Private Information Retrieval Protocols for Distributed Storage
We consider private information retrieval (PIR) for distributed storage
systems (DSSs) with noncolluding nodes where data is stored using a non maximum
distance separable (MDS) linear code. It was recently shown that if data is
stored using a particular class of non-MDS linear codes, the MDS-PIR capacity,
i.e., the maximum possible PIR rate for MDS-coded DSSs, can be achieved. For
this class of codes, we prove that the PIR capacity is indeed equal to the
MDS-PIR capacity, giving the first family of non-MDS codes for which the PIR
capacity is known. For other codes, we provide asymmetric PIR protocols that
achieve a strictly larger PIR rate compared to existing symmetric PIR
protocols.Comment: To be presented at 2018 IEEE Information Theory Workshop (ITW'18).
See arXiv:1808.09018 for its extended versio
Robust Private Information Retrieval on Coded Data
We consider the problem of designing PIR scheme on coded data when certain
nodes are unresponsive. We provide the construction of -robust PIR schemes
that can tolerate up to unresponsive nodes. These schemes are adaptive
and universally optimal in the sense of achieving (asymptotically) optimal
download cost for any number of unresponsive nodes up to
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