# The Capacity of Private Information Retrieval from Heterogeneous Uncoded Caching Databases

## TL;DR

This paper investigates the optimal private information retrieval strategy from multiple databases with different storage capacities, revealing that heterogeneity does not reduce the maximum achievable download efficiency.

## Contribution

It characterizes the optimal PIR download cost for heterogeneous storage databases and shows it equals the homogeneous case, providing explicit placement for three databases.

## Key findings

- Optimal PIR download cost matches the homogeneous case.
- Heterogeneity in storage does not reduce PIR capacity.
- Explicit content placement for three databases is provided.

## Abstract

We consider private information retrieval (PIR) of a single file out of $K$ files from $N$ non-colluding databases with heterogeneous storage constraints $\mathbf{m}=(m_1, \cdots, m_N)$. The aim of this work is to jointly design the content placement phase and the information retrieval phase in order to minimize the download cost in the PIR phase. We characterize the optimal PIR download cost as a linear program. By analyzing the structure of the optimal solution of this linear program, we show that, surprisingly, the optimal download cost in our heterogeneous case matches its homogeneous counterpart where all databases have the same average storage constraint $\mu=\frac{1}{N} \sum_{n=1}^{N} m_n$. Thus, we show that there is no loss in the PIR capacity due to heterogeneity of storage spaces of the databases. We provide the optimum content placement explicitly for $N=3$.