The capacity of cache aided private information retrieval

Abstract

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 information-theoretically optimal.

Capacity-Achieving Private Information Retrieval Codes With Optimal Message Size and Upload Cost

“…The question we wish to address in this section is what the root cause is for these improvements. It is clear that the existing codes in the literature, such as [1,2,12,14,16,21], are all symmetric, while our proposed code is not symmetric. It is thus natural to suspect that this symmetry vs. asymmetry relation is the root cause, however, in order to better understand this issue, we have to identify and evaluate carefully the symmetry relations in the problem.…”

“…In the previous works where the PIR capacity is concerned, such as [1,2,12,14,[16][17][18], it is usually assumed that the message length L is sufficiently large (L is allowed to go to infinity). As a consequence, the corresponding code constructions in the literature are usually built by recursively layering message symbols and parity symbols using symmetry relations, resulting in codes that can only be applied on very long messages.…”

Cross Subspace Alignment and the Asymptotic Capacity of $X$ -Secure $T$ -Private Information Retrieval

“…In particular, capacity is known for disjoint colluding sets [4]. The rapidly growing body of literature in this area has produced capacity results for PIR under a rich variety of constraints [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. However, the capacity for the natural setting of secure storage remains unknown, and relatively unexplored.…”

Single-Server Single-Message Online Private Information Retrieval with Side Information

“…The most relevant to our paper is the line of work that focuses on setting with multiple retrieved messages [8], [12], [13] as well as settings in which the user access to certain files as side information before the information retrieval process begins. The side information settings have been studied in [2], [3] for the single server setting and in [4]- [8] for the multi-server setting.…”