Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On private information retrieval array codes   Given a database, the private information retrieval (PIR) protocol allows a
user to make queries to several servers and retrieve a certain item of the
database via the feedbacks, without revealing the privacy of the specific item
to any single server. Classical models of PIR protocols require that each
server stores a whole copy of the database. Recently new PIR models are
proposed with coding techniques arising from distributed storage system. In
these new models each server only stores a fraction $1/s$ of the whole
database, where $s>1$ is a given rational number. PIR array codes are recently
proposed by Fazeli, Vardy and Yaakobi to characterize the new models. Consider
a PIR array code with $m$ servers and the $k$-PIR property (which indicates
that these $m$ servers may emulate any efficient $k$-PIR protocol). The central
problem is to design PIR array codes with optimal rate $k/m$. Our contribution
to this problem is three-fold. First, for the case $1<s\le 2$, although PIR
array codes with optimal rate have been constructed recently by Blackburn and
Etzion, the number of servers in their construction is impractically large. We
determine the minimum number of servers admitting the existence of a PIR array
code with optimal rate for a certain range of parameters. Second, for the case
$s>2$, we derive a new upper bound on the rate of a PIR array code. Finally,
for the case $s>2$, we analyze a new construction by Blackburn and Etzion and
show that its rate is better than all the other existing constructions.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con