Private Information Delivery
- MoE

We introduce the problem of private information delivery (PID), comprised of messages, a user, and servers (each holds messages) that wish to deliver one out of messages to the user privately, i.e., without revealing the delivered message index to the user. The information theoretic capacity of PID, , is defined as the maximum number of bits of the desired message that can be privately delivered per bit of total communication to the user. For the PID problem with messages, servers, messages stored per server, and , we provide an achievable scheme of rate and an information theoretic converse of rate , i.e., the PID capacity satisfies . This settles the capacity of PID when is an integer. When is not an integer, we show that the converse rate of is achievable if , and the achievable rate of is optimal if . Otherwise if , we give an improved achievable scheme and prove its optimality for several small settings.
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