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Breaking the MDS-PIR Capacity Barrier via Joint Storage Coding
Open AccessFeature PaperArticle

The Capacity of Private Information Retrieval from Decentralized Uncoded Caching Databases

Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA
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Information 2019, 10(12), 372; https://doi.org/10.3390/info10120372
Received: 5 August 2019 / Revised: 9 October 2019 / Accepted: 12 November 2019 / Published: 28 November 2019
(This article belongs to the Special Issue Private Information Retrieval: Techniques and Applications)
We consider the private information retrieval (PIR) problem from decentralized uncoded caching databases. There are two phases in our problem setting, a caching phase, and a retrieval phase. In the caching phase, a data center containing all the K files, where each file is of size L bits, and several databases with storage size constraint μ K L bits exist in the system. Each database independently chooses μ K L bits out of the total K L bits from the data center to cache through the same probability distribution in a decentralized manner. In the retrieval phase, a user (retriever) accesses N databases in addition to the data center, and wishes to retrieve a desired file privately. We characterize the optimal normalized download cost to be D * = n = 1 N + 1 N n 1 μ n 1 ( 1 μ ) N + 1 n 1 + 1 n + + 1 n K 1. We show that uniform and random caching scheme which is originally proposed for decentralized coded caching by Maddah-Ali and Niesen, along with Sun and Jafar retrieval scheme which is originally proposed for PIR from replicated databases surprisingly results in the lowest normalized download cost. This is the decentralized counterpart of the recent result of Attia, Kumar, and Tandon for the centralized case. The converse proof contains several ingredients such as interference lower bound, induction lemma, replacing queries and answering string random variables with the content of distributed databases, the nature of decentralized uncoded caching databases, and bit marginalization of joint caching distributions. View Full-Text
Keywords: private information retrieval (PIR); decentralized caching; uncoded caching; PIR capacity private information retrieval (PIR); decentralized caching; uncoded caching; PIR capacity
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MDPI and ACS Style

Wei, Y.-P.; Arasli, B.; Banawan, K.; Ulukus, S. The Capacity of Private Information Retrieval from Decentralized Uncoded Caching Databases. Information 2019, 10, 372.

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