This paper revisited the problem of Private Information Retrieval (PIR), where there are $N$ replicated non-communicating databases containing the same $M$ messages and a user who wishes to retrieve one of the messages without revealing the wanted message's index to the databases. However, we assume a block-fading additive white Gaussian noise multiple access channel (AWGN MAC) linking the user and the databases. Previous work \cite{shmuel2021private} presented a joint channel-PIR scheme, utilizing the Compute and Forward protocol, showing the potential of a joint channel-PIR scheme over a separated one. This paper proposes an improved joint scheme 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. Specifically, the 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, the analysis demonstrates that the improved rate exhibits only a finite gap from the unconstrained channel capacity -- one bit per second per Hz as $N$ increases.

翻译：本文重新审视了私密信息检索（PIR）问题，其中包含N个复制且非通信的数据库，存储着相同的M条消息，用户希望在不向数据库泄露所请求消息索引的情况下检索其中一条消息。然而，我们假设用户与数据库之间存在块衰落加性高斯白噪声多址接入信道（AWGN MAC）。先前的工作\cite{shmuel2021private}提出了一种利用计算转发协议的信道-PIR联合方案，展示了联合信道-PIR方案相较于分离方案的潜力。本文提出了一种针对N个数据库在块衰落AWGN下PIR问题的改进联合方案。与C&F协议不同，我们的方案在降低计算复杂度的同时，改进了控制可达速率的缩放律。具体而言，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似，且优于基于C&F的方法。此外，分析表明，该改进速率与无约束信道容量之间仅存在有限差距——当N增大时，差距为每秒每赫兹一比特。