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 mods Gaussian wiretap channel (GWC). Then, we propose an explicit shaping scheme to remove this mods front 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. Index Terms-Gaussian wiretap channel, polar lattice, secrecy capacity, semantic security. Polar codes [7] have shown their great potential in solving the wiretap coding problem. The polar coding scheme proposed in [8] , combined with the block Markov coding technique [9] , was proved to achieve the strong secrecy capacity 0018-9448
In REF , a wiretap scheme was shown to achieve the semantic secrecy capacity of AWGN wiretap channels, albeit in a completely different manner than the previously mentioned five papers.
Achieving Secrecy Capacity of the Gaussian Wiretap Channel With Polar Lattices
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Computer Science Mathematics