We consider the problem of private information retrieval (PIR) from N non-colluding and replicated databases when the user is equipped with a cache that holds an uncoded fraction r from each of the K stored messages in the databases. We assume that the databases are unaware of the cache content. We investigate D * (r) the optimal download cost normalized with the message size as a function of K, N , r. For a fixed K, N , we develop an inner bound (converse bound) for the D * (r) curve. The inner bound is a piece-wise linear function in r that consists of K line segments. For the achievability, we develop explicit schemes that exploit the cached bits as side information to achieve K − 1 non-degenerate corner points. These corner points differ in the number of cached bits that are used to generate one side information equation. We obtain an outer bound (achievability) for any caching ratio by memory-sharing between these corner points. Thus, the outer bound is also a piece-wise linear function in r that consists of K line segments. The inner and the outer bounds match in general for the cases of very low caching ratio (r ≤ 1 1+N +N 2 +···+N K−1 ) and very high caching ratio (r ≥ K−2 (N +1)K+N 2 −2N −2 ). As a corollary, we fully characterize the optimal download cost caching ratio tradeoff for K = 3. For general K, N , and r, we show that the largest gap between the achievability and the converse bounds is 1 6 . Our results show that the download cost can be reduced beyond memory-sharing if the databases are unaware of the cached content.
We consider the problem of private information retrieval (PIR) of a single message out of K messages from N replicated and non-colluding databases where a cacheenabled user (retriever) of cache-size M possesses side information in the form of full messages that are partially known to the databases. In this model, the user and the databases engage in a two-phase scheme, namely, the prefetching phase where the user acquires side information and the retrieval phase where the user downloads desired information. In the prefetching phase, the user receives m n full messages from the nth database, under the cache memory size constraint N n=1 m n ≤ M . In the retrieval phase, the user wishes to retrieve a message such that no individual database learns anything about the identity of the desired message. In addition, the identities of the side information messages that the user did not prefetch from a database must remain private against that database. Since the side information provided by each database in the prefetching phase is known by the providing database and the side information must be kept private against the remaining databases, we coin this model as partially *
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