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- W2950812103 abstract "We consider the problem of multi-message private information retrieval (MPIR) from $N$ non-communicating replicated databases. In MPIR, the user is interested in retrieving $P$ messages out of $M$ stored messages without leaking the identity of the retrieved messages. The information-theoretic sum capacity of MPIR $C_s^P$ is the maximum number of desired message symbols that can be retrieved privately per downloaded symbol. For the case $P geq frac{M}{2}$, we determine the exact sum capacity of MPIR as $C_s^P=frac{1}{1+frac{M-P}{PN}}$. The achievable scheme in this case is based on downloading MDS-coded mixtures of all messages. For $P leq frac{M}{2}$, we develop lower and upper bounds for all $M,P,N$. These bounds match if the total number of messages $M$ is an integer multiple of the number of desired messages $P$, i.e., $frac{M}{P} in mathbb{N}$. In this case, $C_s^P=frac{1-frac{1}{N}}{1-(frac{1}{N})^{M/P}}$. The achievable scheme in this case generalizes the single-message capacity achieving scheme to have unbalanced number of stages per round of download. For all the remaining cases, the difference between the lower and upper bound is at most $0.0082$, which occurs for $M=5$, $P=2$, $N=2$. Our results indicate that joint retrieval of desired messages is more efficient than successive use of single-message retrieval schemes." @default.
- W2950812103 created "2019-06-27" @default.
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- W2950812103 date "2017-02-06" @default.
- W2950812103 modified "2023-09-27" @default.
- W2950812103 title "Multi-Message Private Information Retrieval: Capacity Results and Near-Optimal Schemes" @default.
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