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The Capacity of Private Information Retrieval

Abstract

In the private information retrieval (PIR) problem a user wishes to retrieve, as efficiently as possible, one out of KK messages from NN non-communicating databases (each holds all KK messages) while revealing nothing about the identity of the desired message index to any individual database. The information theoretic capacity of PIR is the maximum number of bits of desired information that can be privately retrieved per bit of downloaded information. For KK messages and NN databases, we show that the PIR capacity is (1+1/N+1/N2++1/NK1)1(1+1/N+1/N^2+\cdots+1/N^{K-1})^{-1}. A remarkable feature of the capacity achieving scheme is that if it is projected onto any subset of messages by eliminating the remaining messages, it also achieves the PIR capacity for that subset of messages.

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