New Results on the Storage-Retrieval Tradeoff in Private Information Retrieval Systems

In a private information retrieval (PIR) system, the user needs to retrieve one of possible messages from set storage servers, but wishes keep identity requested message any given server. Existing efforts in this area have made it clear that efficiency will be impacted significantly by amount space allowed at servers. work, we consider tradeoff between cost and cost. We first present three fundamental results: 1) regime-wise approximate characterization optimal with factor two, 2) cyclic permutation lemma can produce more sophisticated codes simpler base codes, 3) relaxed entropic linear program (LP) lower bound has polynomial complexity. Equipped lemma, then propose two novel code constructions, applying obtain new storage-retrieval points. Furthermore, derive explicit bounds utilizing only subset constraints LP systematic manner. Though upper do not lead better approximation uniformly, they are tighter than existing art some regimes.