The problem of cache enabled private information retrieval (PIR) is considered in which a user wishes to privately retrieve one out of K messages, each of size L bits from N distributed databases. The user has a local cache of storage SL bits which can be used to store any function of the K messages. The main contribution of this work is the exact characterization of the capacity of cache enabled PIR as a function of the storage parameter S. In particular, for a given cache storage parameter S, the information-theoretically optimal download cost D * (S)/L (or the inverse of capacity) is shown to be equal to (1 − S K ) 1 + 1 N + . . . + 1 N K−1 . Special cases of this result correspond to the settings when S = 0, for which the optimal download cost was shown by Sun and Jafar to be 1 + 1 N + . . . + 1 N K−1 , and the case when S = K, i.e., cache size is large enough to store all messages locally, for which the optimal download cost is 0. The intermediate points S ∈ (0, K) can be readily achieved through a simple memory-sharing based PIR scheme. The key technical contribution of this work is the converse, i.e., a lower bound on the download cost as a function of storage S which shows that memory sharing is informationtheoretically optimal.
In REF , the side information can be any function of the database, and is known to all the servers.
The capacity of cache aided private information retrieval
2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Computer Science Mathematics