Private Information Retrieval From a Cellular Network With Caching at the Edge

Abstract

We consider the problem of downloading content from a cellular network where content is cached at the wireless edge while achieving privacy. In particular, we consider private information retrieval (PIR) of content from a library of files, i.e., the user wishes to download a file and does not want the network to learn any information about which file she is interested in. To reduce the backhaul usage, content is cached at the wireless edge in a number of small-cell base stations (SBSs) using maximum distance separable codes. We propose a PIR scheme for this scenario that achieves privacy against a number of spy SBSs that (possibly) collaborate. The proposed PIR scheme is an extension of a recently introduced scheme by Kumar et al. to the case of multiple code rates, suitable for the scenario where files have different popularities. We then derive the backhaul rate and optimize the content placement to minimize it. We prove that uniform content placement is optimal, i.e., all files that are cached should be stored using the same code rate. This is in contrast to the case where no PIR is required. Furthermore, we show numerically that popular content placement is optimal for some scenarios.

Private Information Retrieval in Wireless Coded Caching

“…We further prove that uniform content allocation is optimal, in contrast to the case of no PIR, where uniform content allocation is suboptimal in general [3]. Compared to our recently proposed protocol [12], the presented protocol gives a reduced backhaul rate. We give results for a Poisson point process (PPP) deployment model where SBSs are distributed over the plane according to a PPP.…”

“…Note that if the protocols give a backhaul rate above one, we plot one, since a backhaul rate of one can be obtained by downloading the file directly from the MBS. As can be seen, the proposed protocol gives a lower backhaul rate compared to the protocol from [12]. In the figure, we give the optimal values of n and k = 1/µ for M = 50.…”

“…In the figure, we plot the optimized backhaul rate from (5) (solid lines) as a function of the density λ for F = 200 files, α = 0.7, r u = 60 meters, different cache size constraint M , and T = 2. For comparison, we also plot the curves for popular content placement, i.e., with µ max = µ min = 1 in (5) (dashed lines), and the optimal backhaul rate of the protocol from [12] (dotted lines). Note that if the protocols give a backhaul rate above one, we plot one, since a backhaul rate of one can be obtained by downloading the file directly from the MBS.…”

“…The number of queries n and the threshold b th need be optimized. This is in contrast to the protocol in [12] where a fixed b th = 1 was used. The intuition is that when no SBSs are within communication range, it is beneficial to download the file with no redundancy directly from the MBS.…”

“…The query matrix [12] where a fixed d l = k max was used for all queries. In response to each query, a SBS (or the MBS) sends back a response vector r (l) = (r The concept of information-theoretic PIR is formally defined as follows.…”