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 ΞΌKL bits exist in the
system. Each database independently chooses ΞΌKL bits out of the total
KL 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 LDβ=βn=1N+1β(nβ1Nβ)ΞΌnβ1(1βΞΌ)N+1βn(1+n1β+β―+nKβ11β). 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 result 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.Comment: Submitted for publication, November 201