Improved Storage for Efficient Private Information Retrieval

Abstract

We consider the problem of private information retrieval from N storage-constrained databases. In this problem, a user wishes to retrieve a single message out of M messages (of size L) without revealing any information about the identity of the message to individual databases. Each database stores µM L symbols, i.e., a µ fraction of the entire library, where 1 N ≤ µ ≤ 1. Our goal is to characterize the optimal tradeoff curve for the storage cost (captured by µ) and the normalized download cost (D/L). We show that the download cost can be reduced by employing a hybrid storage scheme that combines MDS coding ideas with uncoded partial replication ideas. When there is no coding, our scheme reduces to Attia-Kumar-Tandon storage scheme, which was initially introduced by Maddah-Ali-Niesen in the context of the caching problem, and when there is no uncoded partial replication, our scheme reduces to Banawan-Ulukus storage scheme; in general, our scheme outperforms both.

Capacity-Achieving Private Information Retrieval Schemes from Uncoded Storage Constrained Servers with Low Sub-packetization

“…Though repetition coding can offer simplicity in designing PIR schemes and the high immunity against server failures, it suffers from extremely large storage cost. The storage cost in a PIR system has been widely investigated in terms of the coding structures in the storage design, such as specific Maximum Distance Separable (MDS) codes [3], [25], [37], an uncoded storage [26], [1], [31], and other more complicated coding techniques [20], [10], [5], [19], [36], [14], [2]. Moreover, the tradeoff between the storage cost and retrieval rate was considered without any explicit constraints on the storage codes [24], [29], [30].…”

“…by the independence of the files(2) and the fact that queries are independent of the files(8); (e) and (f ) follow by simply changing the summation indices; (g) follows fromK⊆[1:K]\{θ},|K|=k H(W θ |Z N ) = K−1 k H(W θ |Z N ); (h) follows from the definition of λ n in (59).Notice that when n ∈ [0 : N − 1] and k = K − 1, all the files W 1:K are presented in the conditions of each entropy function in T (n, k). Since the answers A[θ] [1:N ]\N is a function of Q [θ][1:N ]\N and W 1:K by (9), we have T (n, K − 1) = 0.…”

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

“…Attia et al considered the case when the storage servers can only store uncoded segments of the messages [7], [8], and derived the full storage-retrieval tradeoff in such systems. A generalized code construction unifying the two codes was presented more recently in [9]. Mathematically, we use α to denote the normalized average storage per server per message bit, and β for the normalized average download cost per server by message bit (the precise definitions are given in Section II).…”

“…2) A cyclic permutation lemma that can produce more sophisticated codes from simpler ones: This is a general technique, and it can be shown that uncoded storage PIR code [7], [8] can be obtained directly from the code in [4] with this lemma, and the generalized MDS-PIR code [9] can be obtained from that in [6].…”

On the Storage Cost of Private Information Retrieval

“…In two recent works [11,22], the tradeoff was considered without any structural constraints on the storage or retrieval codes for the special case of two databases and two messages, and it was found that non-linear codes can provide further improvement over linear codes. Other notable efforts can be found in [23][24][25][26][27] and references therein.…”