Introduced by Sadeh et al., the K-star-graph private information retrieval (PIR) problem, so-labeled because the storage graph is a star-graph with K leaf nodes, is comprised of K messages that are stored separately (one-each) at K dedicated servers, and a universal server that stores all K messages, for a total of K + 1 servers. While it is one of the simplest PIR settings to describe, the capacity CK of K-star-graph PIR is open for K ≥ 4. We study the critical K = 4 setting, for which prior work establishes the bounds 2/5 ≤ C4 ≤ 3/7. As our main contribution, we characterize the exact capacity of 4-star-graph PIR as C4 = 5/12, thus improving upon both the prior lower- bound as well as the prior upper-bound. The main technical challenge resides in the new converse bound, whose non-trivial structure is deduced indirectly from the achievable schemes that emerge from the study of a finer tradeoff between the download costs from the dedicated servers versus the universal server. A sharp characterization of this tradeoff is also obtained for K = 4.
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Two-Level Private Information Retrieval
In the conventional robust T -colluding private information retrieval (PIR) system, the user needs to retrieve one of the possible messages while keeping the identity of the requested message private from any T colluding servers. Motivated by the possible heterogeneous privacy requirements for different messages, we consider the ( N,T1:K1,T2:K2 ) two-level PIR system, where K1 messages need to be retrieved privately against T1 colluding servers, and all the messages need to be retrieved privately against T2 colluding servers where T2≤T1 . We obtain a lower bound to the capacity by proposing a novel coding scheme, namely the non-uniform successive cancellation scheme. A capacity upper bound is also derived. The gap between the upper bound and the lower bound is analyzed, and shown to vanish when T1=T2 .
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- NSF-PAR ID:
- 10295050
- Date Published:
- Journal Name:
- 2021 IEEE International Symposium on Information Theory (ISIT)
- Page Range / eLocation ID:
- 1919 to 1924
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ISIT45174.2021.9518167
