The Capacity of Uncoded Storage Constrained PIR

Mohamed Adel Attia, Deepak Kumar, Ravi Tandon

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


Private information retrieval (PIR) allows a user to retrieve a desired message out of K possible messages from N databases (DBs) without revealing the identity of the desired message. In this work, we consider the problem of PIR from uncoded storage constrained DBs. Each DB has a storage capacity of mu KL bits, where L is the size of each message in bits, and muin[1/N, 1] is the normalized storage. In the storage constrained PIR problem, there are two key challenges: a) construction of communication efficient schemes through storage content design at each DB that allow download efficient PIR; and b characterizing the optimal download cost via information-theoretic lower bounds. The novel aspect of this work is to characterize the optimum download cost of PIR with storage constrained DBs for any value of storage. In particular, for any (N, K), we show that the optimal tradeoff between storage (mu) and the download cost (D(mu)) is given by the lower convex hull of the pairs (frac t N(1+frac 1 t+frac 1 t 2+cdots+frac 1 t K-1)) for t = 1,2,..., N. The main contribution of this paper is the converse proof, i.e., obtaining lower bounds on the download cost for PIR as a function of the available storage.

Original languageEnglish (US)
Title of host publication2018 IEEE International Symposium on Information Theory, ISIT 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Print)9781538647806
StatePublished - Aug 15 2018
Event2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States
Duration: Jun 17 2018Jun 22 2018

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2018 IEEE International Symposium on Information Theory, ISIT 2018
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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