LAUSR

We consider the fundamental tradeoff between the storage cost and the download cost in private information retrieval (PIR) systems, without any explicit structural restrictions on the storage codes, such as maximum distance separable codes or uncoded storage. Our focus in this work is on the two extreme points: the point when the storage cost is minimal, and the point when the download cost is minimal. Two novel outer bounds are provided, which have the following implications at these two extreme points. When the messages are stored without any redundancy across the databases, the optimal PIR strategy is to download all the messages; on the other hand, for PIR capacity-achieving codes, each database can reduce the storage cost, from storing all the messages, by no more than one message on average. To better understand the second extreme point, we then focus on the two-message two-database case, and show that a stronger outer bound can be derived through a novel pseudo-message technique. This stronger outer bound suggests that a precise characterization of the storage-download tradeoff may require more sophisticated bounding techniques.