Correction to "Private Information Retrieval Over Gaussian MAC"

Abstract

In the above article \cite{shmuel2021private}, 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 \cite{shmuel2021private} 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 $\cC$, mistakenly suggesting that the user possesses all the required information in advance. % \st{However, this is not the case.} \textcolor{black}{To deal with that, we defined $\phi(\cdot)$ as a one-to-one mapping function between a vector of $l$ information bits and a lattice point $\lambda\in\cC$}. Herein, we present the corrected versions of these theorems.