SPIR with Colluding and Non-Replicated Servers from a Noisy Channel
Amirhossein Shekofteh, Rémi A. Chou · 2024
We study the problem of Symmetric Private Information Retrieval (SPIR) in a scenario with$L$non-replicated and colluding servers, and$M$independent files distributed across these servers. In this setting, communication takes place through a noisy multiple-access channel and a noiseless public channel. The client must retrieve one of the$M$files such that (i) the client's choice must not be revealed to the servers, and (ii) the client must not learn any information about non-selected files. Our main contribution is showing that, for a specific class of channels and without requiring shared randomness among servers, positive rates are achievable even when all the servers collude. Additionally, we present an example of channel where distributing files across multiple servers yields an achievable rate that outperforms a setting where all the files are stored on a single server.