Private information retrieval from a cellular network with caching at the edge

We consider the problem of downloading content from a cellular network that 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 based on generalized Reed-Solomon codes for this scenario that achieves privacy against a number of spy SBSs that collaborate. The proposed PIR scheme is an extension of a scheme by Kumar et al. to the case of multiple code rates, suitable for the scenario where files have different popularities. We 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.