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We propose capacity-achieving schemes for private information retrieval (PIR) from uncoded databases (DBs) with both homogeneous and heterogeneous storage constraints. In the PIR setting, a user queries a set of DBs to privately download a message, where privacy implies that no one DB can infer which message the user desires. In general, a PIR scheme is comprised of storage placement and delivery designs. Previous works have derived the capacity, or infimum download cost, of PIR with uncoded storage placement and sufficient conditions of storage placement to meet capacity. However, the currently proposed storage placement designs require splitting each message into an exponential number of sub-messages with respect to the number of DBs. In this work, when DBs have the same storage constraint, we propose two simple storage placement designs that satisfy the capacity conditions. Then, for more general heterogeneous storage constraints, we translate the storage placement design process into a “filling problem”. We design an iterative algorithm to solve the filling problem where, in each iteration, messages are partitioned into sub-messages and stored at subsets of DBs. All of our proposed storage placement designs require a number of sub-messages per message at most equal to the number of DBs.
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On Single Server Private Information Retrieval With Private Coded Side Information
Motivated by an open problem and a conjecture, this work studies the problem of single server private information retrieval with private coded side information (PIR-PCSI) that was recently introduced by Heidarzadeh et al. The goal of PIR-PCSI is to allow a user to efficiently retrieve a desired message Wθ, which is one of K independent messages that are stored at a server, while utilizing private side information of a linear combination of a uniformly chosen size-M subset (S ⊂ [K]) of messages. The settings PIR-PCSI-I and PIR-PCSI-II correspond to the constraints that θ is generated uniformly from [K]\S, and S, respectively. In each case, (θ, S) must be kept private from the server. The capacity is defined as the supremum over message and field sizes, of achievable rates (number of bits of desired message retrieved per bit of download) and is characterized by Heidarzadeh et al. for PIR-PCSI-I in general, and for PIR- PCSI-II for M > (K + 1)/2 as (K − M + 1)−1. For 2 ≤ M ≤ (K + 1)/2 the capacity of PIR-PCSI-II remains open, and it is conjectured that even in this case the capacity is (K − M + 1)−1. We show the capacity of PIR-PCSI-II is equal to 2/K for 2 ≤ M ≤ K+1, which is strictly larger 2 than the conjectured value, and does not depend on M within this parameter regime. Remarkably, half the side-information is found to be redundant. We also characterize the infimum capacity (infimum over fields instead of supremum), and the capacity with private coefficients. The results are generalized to PIR-PCSI-I (θ ∈ [K] \ S) and PIR-PCSI (θ ∈ [K]) settings.
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- Award ID(s):
- 1907053
- PAR ID:
- 10466692
- Editor(s):
- Matthieu Bloch
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Information Theory
- Volume:
- 69
- Issue:
- 5
- ISSN:
- 0018-9448
- Page Range / eLocation ID:
- 3263 to 3284
- Subject(s) / Keyword(s):
- Capacity, Private Information Retrieval (PIR), coded side information (CSI), interference alignment.
- 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
- Journal Article:
- https://doi.org/10.1109/TIT.2023.3253078
