Achieving Secrecy Capacity of the Gaussian Wiretap Channel With Polar Lattices
Линг Лиу, Yanfei Yan, Cong Ling · IEEE Transactions on Information Theory · 2018
In this paper, an explicit scheme of wiretap coding based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. First, polar lattices are used to construct secrecy-good lattices for the mod-ΛsGaussian wiretap channel (GWC). Then, we propose an explicit shaping scheme to remove this mod-Λsfront end and extend polar lattices to the genuine GWC. The shaping technique is based on the lattice Gaussian distribution, which leads to a binary asymmetric channel at each level for the multilevel lattice codes. By employing the asymmetric polar coding technique, we construct an AWGN-good lattice and a secrecy-good lattice with optimal shaping simultaneously. As a result, the encoding complexity for the sender and the decoding complexity for the legitimate receiver are both O(N log N log (log N)) . The proposed scheme is proven to be semantically secure.