On the Capacity of Latent Variable Private Information Retrieval

In latent-variable private information retrieval (LVPIR), a user wishes to retrieve one out of K messages (indexed by theta) without revealing any information about a sensitive latent attribute (modeled by a latent variable S correlated with theta). While conventional PIR protocols, which keep theta private, also suffice for hiding S, they can be too costly in terms of the download overhead. In this paper, we characterize the capacity (equivalently, the optimal download cost) of LV-PIR as a function of the distribution P-S vertical bar theta. We present a converse proof that yields a lower bound on the optimal download cost, and a matching achievable scheme. The optimal scheme, however, involves an exhaustive search over subset queries and over all messages, which can be computationally prohibitive. We further present two low-complexity, albeit sub-optimal, schemes that also outperform the conventional PIR solution.