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The Capacity of Cache Aided Private Information Retrieval

21 June 2017
Ravi Tandon
ArXiv (abs)PDFHTML
Abstract

The problem of cache enabled private information retrieval (PIR) is considered in which a user wishes to privately retrieve one out of KKK messages, each of size LLL bits from NNN distributed databases. The user has a local cache of storage SLSLSL bits which can be used to store any function of the KKK messages. The main contribution of this work is the exact characterization of the capacity of cache aided PIR as a function of the storage parameter SSS. In particular, for a given cache storage parameter SSS, the information-theoretically optimal download cost D∗(S)/LD^{*}(S)/LD∗(S)/L (or the inverse of capacity) is shown to be equal to (1−SK)(1+1N+…+1NK−1)(1- \frac{S}{K})\left(1+ \frac{1}{N}+ \ldots + \frac{1}{N^{K-1}}\right)(1−KS​)(1+N1​+…+NK−11​). Special cases of this result correspond to the settings when S=0S=0S=0, for which the optimal download cost was shown by Sun and Jafar to be (1+1N+…+1NK−1)\left(1+ \frac{1}{N}+ \ldots + \frac{1}{N^{K-1}}\right)(1+N1​+…+NK−11​), and the case when S=KS=KS=K, i.e., cache size is large enough to store all messages locally, for which the optimal download cost is 000. The intermediate points S∈(0,K)S\in (0, K)S∈(0,K) can be readily achieved through a simple memory-sharing based PIR scheme. The key technical contribution of this work is the converse, i.e., a lower bound on the download cost as a function of storage SSS which shows that memory sharing is information-theoretically optimal.

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