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We consider the storage-retrieval rate tradeoff in private informationretrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostlyon the canonical two-message two-database case, for which a coding scheme basedon random codebook generation and the binning technique is proposed. Thiscoding scheme reveals a hidden connection between PIR and the classic multipledescription source coding problem. We first show that when the retrieval rateis kept optimal, the proposed non-linear scheme can achieve better performanceover any linear scheme. Moreover, a non-trivial storage-retrieval rate tradeoffcan be achieved beyond space-sharing between this extreme point and the otheroptimal extreme point, achieved by the retrieve-everything strategy. We furthershow that with a method akin to the expurgation technique, one can extract azero-error PIR code from the random code. Outer bounds are also studied andcompared to establish the superiority of the non-linear codes over linearcodes.

A Shannon-Theoretic Approach to the Storage-Retrieval Tradeoff in PIR Systems