Polar Lattices for Strong Secrecy Over the Mod-$\Lambda$ Gaussian Wiretap Channel

Abstract

Polar lattices, which are constructed from polar codes, are provably good for the additive white Gaussian noise (AWGN) channel. In this work, we propose a new polar lattice construction that achieves the secrecy capacity under the strong secrecy criterion over the mod-$\Lambda$ Gaussian wiretap channel. This construction leads to an AWGN-good lattice and a secrecy-good lattice simultaneously. The design methodology is mainly based on the equivalence in terms of polarization between the $\Lambda/\Lambda'$ channel in lattice coding and the equivalent channel derived from the chain rule of mutual information in multilevel coding.