Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Capacity-Achieving PIR Schemes with Optimal Sub-Packetization   Suppose a database containing $M$ records is replicated across $N$ servers,
and a user wants to privately retrieve one record by accessing the servers such
that identity of the retrieved record is secret against any up to $T$ servers.
A scheme designed for this purpose is called a private information retrieval
(PIR) scheme. In practice, capacity-achieving and small sub-packetization are
both desired for PIR schemes, because the former implies the highest download
rate and the latter usually means simple realization.
  For general values of $N,T,M$, the only known capacity-achieving PIR scheme
was designed by Sun and Jafar in 2016 with sub-packetization $N^M$. In this
paper, we design a linear capacity-achieving PIR scheme with much smaller
sub-packetization $dn^{M-1}$, where $d={\rm gcd}(N,T)$ and $n=N/d$.
Furthermore, we prove that for any linear capacity-achieving PIR scheme it must
have sub-packetization no less than $dn^{M-1}$, implying our scheme has the
optimal sub-packetization. Moreover, comparing with Sun and Jafar's scheme, our
scheme reduces the field size by a factor of $\frac{1}{Nd^{M-2}}$.

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The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn