Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymmetric Leaky Private Information Retrieval   Information-theoretic formulations of the private information retrieval (PIR)
problem have been investigated under a variety of scenarios. Symmetric private
information retrieval (SPIR) is a variant where a user is able to privately
retrieve one out of $K$ messages from $N$ non-colluding replicated databases
without learning anything about the remaining $K-1$ messages. However, the goal
of perfect privacy can be too taxing for certain applications. In this paper,
we investigate if the information-theoretic capacity of SPIR (equivalently, the
inverse of the minimum download cost) can be increased by relaxing both user
and DB privacy definitions. Such relaxation is relevant in applications where
privacy can be traded for communication efficiency. We introduce and
investigate the Asymmetric Leaky PIR (AL-PIR) model with different privacy
leakage budgets in each direction. For user privacy leakage, we bound the
probability ratios between all possible realizations of DB queries by a
function of a non-negative constant $\epsilon$. For DB privacy, we bound the
mutual information between the undesired messages, the queries, and the
answers, by a function of a non-negative constant $\delta$. We propose a
general AL-PIR scheme that achieves an upper bound on the optimal download cost
for arbitrary $\epsilon$ and $\delta$. We show that the optimal download cost
of AL-PIR is upper-bounded as $D^{*}(\epsilon,\delta)\leq
1+\frac{1}{N-1}-\frac{\delta e^{\epsilon}}{N^{K-1}-1}$. Second, we obtain an
information-theoretic lower bound on the download cost as
$D^{*}(\epsilon,\delta)\geq
1+\frac{1}{Ne^{\epsilon}-1}-\frac{\delta}{(Ne^{\epsilon})^{K-1}-1}$. The gap
analysis between the two bounds shows that our AL-PIR scheme is optimal when
$\epsilon =0$, i.e., under perfect user privacy and it is optimal within a
maximum multiplicative gap of $\frac{N-e^{-\epsilon}}{N-1}$ for any
$(\epsilon,\delta)$.

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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol