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  1. We consider the storage–retrieval rate trade-off in private information retrieval (PIR) systems using a Shannon-theoretic approach. Our focus is mostly on the canonical two-message two-database case, for which a coding scheme based on random codebook generation and the binning technique is proposed. This coding scheme reveals a hidden connection between PIR and the classic multiple description source coding problem. We first show that when the retrieval rate is kept optimal, the proposed non-linear scheme can achieve better performance over any linear scheme. Moreover, a non-trivial storage-retrieval rate trade-off can be achieved beyond space-sharing between this extreme point and the other optimal extreme point, achieved by the retrieve-everything strategy. We further show that with a method akin to the expurgation technique, one can extract a zero-error PIR code from the random code. Outer bounds are also studied and compared to establish the superiority of the non-linear codes over linear codes. 
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  2. We consider the cache-aided multiuser private information retrieval (MuPIR) problem with a focus on the special case of two messages, two users and arbitrary number of databases where the users have distinct demands of the messages. We characterize the optimal memory-load trade-off for the considered MuPIR problem by proposing a novel achievable scheme and a tight converse. The proposed achievable scheme uses the idea of cache-aided interference alignment (CIA) developed in the literature by the same authors. The proposed converse uses a tree-like decoding structure to incorporate both the decodability and privacy requirements of the users. While the optimal characterization of the cache-aided MuPIR problem is challenging in general, this work provides insight into understanding the general structure of the cache-aided MuPIR problem. 
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  3. In the coded caching literature, the notion of privacy is considered only against demands. On the motivation that multi-round transmissions almost appear everywhere in real communication systems, this paper formulates the coded caching problem with private demands and caches. Only one existing private caching scheme, which is based on introducing virtual users, can preserve the privacy of demands and caches simultaneously, but at the cost of an extremely large subpacketization exponential in the product of the number of users (K) and files (N) in the system. In order to reduce the subpacketization while satisfying the privacy constraints, we propose a novel approach which constructs private coded caching schemes through private information retrieval (PIR). Based on this approach, we propose novel schemes with private demands and caches which have a subpacketization level in the order exponential with K instead of NK in the virtual user scheme. As a by-product, for the coded caching problem with private demands, a private coded caching scheme could be obtained from the proposed approach, which generally improves the memory-load tradeoff of the private coded caching scheme by Yan and Tuninetti. 
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