Multiround Private Information Retrieval: Capacity and Storage Overhead

TL;DR

This paper proves that multiround PIR schemes do not increase capacity compared to single-round schemes but can reduce storage overhead, especially with non-linear and error-tolerant schemes.

Contribution

It establishes that multiround PIR has the same capacity as single-round PIR, but can achieve lower storage overhead with non-linear, error-tolerant schemes.

Findings

Multiround PIR has the same capacity as single-round PIR.

Multiround schemes can reduce storage overhead.

Non-linear, error-tolerant multiround schemes outperform linear, zero-error schemes in storage efficiency.

Abstract

The capacity has recently been characterized for the private information retrieval (PIR) problem as well as several of its variants. In every case it is assumed that all the queries are generated by the user simultaneously. Here we consider multiround PIR, where the queries in each round are allowed to depend on the answers received in previous rounds. We show that the capacity of multiround PIR is the same as the capacity of single-round PIR (the result is generalized to also include $T$-privacy constraints). Combined with previous results, this shows that there is no capacity advantage from multiround over single-round schemes, non-linear over linear schemes or from $\epsilon$-error over zero-error schemes. However, we show through an example that there is an advantage in terms of storage overhead. We provide an example of a multiround, non-linear, $\epsilon$-error PIR scheme that requires a strictly smaller storage overhead than the best possible with single-round, linear, zero-error PIR schemes.