A Shannon-Theoretic Approach to the Storage–Retrieval Trade-Off in PIR Systems

We consider the storage–retrieval rate trade-off in private information retrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostly on canonical two-message two-database case, for which coding scheme based random codebook generation and binning technique proposed. This reveals hidden connection between PIR classic multiple description source problem. first show that when kept optimal, proposed non-linear can achieve better performance over any linear scheme. Moreover, non-trivial storage-retrieval be achieved beyond space-sharing this extreme point other optimal point, by retrieve-everything strategy. further with method akin to expurgation technique, one extract zero-error code from code. Outer bounds are also studied compared establish superiority of codes codes.