This paper addresses the challenge of the private information retrieval (PIR) problem wherein there are $N$ replicated non-communicating databases containing the same $M$ messages and a user who wants to retrieve one of the messages without revealing the wanted message's index to the databases. In addition, we assume a block-fading additive white Gaussian noise multiple access channel (AWGN MAC) linking the user and the databases. Shmuel's contribution \cite{shmuel2021private}, presenting a joint channel-PIR scheme utilizing the C\&F protocol, has shown the potential of a joint channel-PIR scheme over a separated scheme. In this paper, we propose an improved joint channel-PIR approach tailored for the PIR problem with $N$ databases over a block-fading AWGN. Unlike the C\&F protocol, our scheme offers reduced computational complexity while improving the scaling laws governing the achievable rate. Our achievable rate scales with the number of databases $N$ and the power $P$ similarly to the channel capacity without the privacy constraint and outperforms the C\&F-based approach. Furthermore, our analysis demonstrates that our improved rate exhibits only a finite gap from the channel capacity of one bit as $N$ increases.

翻译：本文针对私有信息检索（PIR）问题展开研究，其中存在$N$个存储相同$M$个消息的复制非通信数据库，用户希望在不泄露目标消息索引的情况下检索其中一条消息。此外，假设用户与数据库之间通过块衰落加性高斯白噪声多址接入信道（AWGN MAC）进行通信。Shmuel等人提出的联合信道-PIR方案\cite{shmuel2021private}基于C\&F协议，展示了联合信道-PIR方案相较于分离方案的潜在优势。本文提出一种改进的联合信道-PIR方法，专门针对$N$个数据库在块衰落AWGN信道下的PIR问题。与C\&F协议不同，本方案在降低计算复杂度的同时优化了可达速率缩放规律。该可达速率随数据库数量$N$和功率$P$的缩放特性与无隐私约束的信道容量相当，且优于基于C\&F的方法。此外，分析表明，随着$N$的增加，本方案改进速率与信道容量的差距始终小于1比特。