🤖 AI Summary
This work investigates the joint communication–privacy optimization problem for private information retrieval (PIR) and symmetric PIR (SPIR) over a block-fading Gaussian multiple-access channel (MAC) with multiple databases. Addressing key bottlenecks—including high computational complexity, rate limitations, and SPIR’s reliance on shared randomness—we propose a low-complexity joint channel–PIR scheme leveraging lattice coding, compute-and-forward, and channel coding co-design; its achievable rate scales with the number of databases (N) and transmit power (P), asymptotically approaching the MAC capacity without privacy constraints, with only a finite gap of 1 bit/sec/Hz. Furthermore, we introduce the first shared-randomness-free joint channel–SPIR scheme, accompanied by two efficient implementations. The proposed frameworks significantly enhance spectral efficiency and practicality under stringent privacy guarantees.
📝 Abstract
This paper revisits the problems of Private Information Retrieval (PIR) and Symmetric PIR (SPIR). In PIR, there are $N$ replicated non-communicating databases containing the same $M$ messages and a user wishing to retrieve one message without revealing the message's index to the databases. SPIR extends this notion further by additionally protecting the privacy of the databases, ensuring that the user learns no information beyond the requested message. 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 (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 and its scaling laws. Specifically, the achievable rate outperforms the C&F-based approach and scales with the number of databases $N$ and the power $P$ similarly to the channel capacity scaling laws extit{without the privacy constraint}. Furthermore, the analysis demonstrates that the improved rate exhibits only a finite gap from this unconstrained channel capacity -- $1$ $bit/sec/Hz$ as $N$ increases. extcolor{black}{Additionally, we provide two SPIR schemes. The first is a modification for our PIR scheme to attain SPIR, 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 using common randomness.