Polar lattices for strong secrecy over the mod-Λ Gaussian wiretap channel

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-Λ 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 Λ/Λ´ channel in lattice coding and the equivalent channel derived from the chain rule of mutual information in multilevel coding.