In this paper, we address the problem of Private Information Retrieval (PIR) over a public Additive White Gaussian Noise (AWGN) channel. In this setting, a curious server—a passive adversary following the protocol but attempting to infer private information from intercepted transmissions—can eavesdrop on other servers' responses, compromising the user's privacy. Prior work on PIR over shared media typically assumed that servers could not overhear each other's transmissions. In contrast, we remove this assumption and consider a fully public channel. We propose a novel joint PIR–channel coding scheme based on nested lattice codes to meet the resulting privacy and reliability challenges. The scheme simultaneously addresses channel noise, ensures user privacy, and protects against curious servers. We demonstrate that a positive PIR rate is achievable even in cases where the channel to the curious server is stronger than the channel to the user.

This paper revisits the problems of Private Information Retrieval (PIR) and Symmetric PIR (SPIR). In PIR, a user retrieves a desired message fromNreplicated, non-communicating databases, each storing the sameMmessages, while preserving the privacy of the requested message index. SPIR extends this notion further by additionally protecting the privacy of the databases, ensuring that the user learns no information beyond the requested message. In this paper, we assume a block-fading Additive White Gaussian Noise Multiple Access Channel (AWGN MAC) linking the user and the databases. Previous work presented a joint channel-PIR scheme utilizing the Compute and Forward (C&F) protocol, demonstrating the potential of a joint PIR-channel coding scheme over a separated one, yet still lagging behind the channel capacity and requiring significant computational complexity. We propose an improved scheme that offers reduced computational complexity while improving the achievable rate for finite parameters, as well as its scaling laws. Specifically, the achievable rate outperforms the C&F-based approach and scales with the number of databasesNand the powerPsimilarly to the channel capacitywithout the privacy constraint. Furthermore, the analysis demonstrates that the improved rate exhibits only a finite gap from this unconstrained channel capacity –$1~bit/sec/Hz$asNincreases. Finally, we provide two SPIR schemes. The first is a modification for our PIR scheme to attain SPIR with no rate loss, which is accomplished by introducing shared common randomness among databases. The second is a novel joint channel-SPIR scheme that utilizes the channel and lattice codes characteristics to nontrivially achieve SPIR without requiring common randomness, at the price of a loss in the achievable rate.

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 [1] 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. In this paper, we propose 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.

In the above article[1], the authors introduced a PIR scheme for the Additive White Gaussian Noise (AWGN) Multiple Access Channel (MAC), both with and without fading. The authors utilized the additive nature of the channel and leveraged the linear properties and structure of lattice codes to retrieve the desired message without the servers acquiring any knowledge about the retrieved message’s index. Theorems 3 and 4 in[1]contain an error arising from the incorrect usage of the modulo operator. Moreover, the proofs assume a one-to-one mapping function,$\phi (\cdot)$, between a message$W_{j}\in \mathbb {F}_{p}^{L}$and the elements of$\mathcal { C}$, mistakenly suggesting that the user possesses all the required information in advance. To deal with that, we defined$\phi (\cdot)$as a one-to-one mapping function between a vector oflinformation bits and a lattice point$\lambda \in {\mathcal { C}}$. Herein, we present the corrected versions of these theorems.