Achieving Secrecy Capacity of the Gaussian Wiretap Channel With Polar Lattices

DOI10.1109/TIT.2018.2794327zbMATH Open1390.94689arXiv1503.02313OpenAlexW2963973138MaRDI QIDQ4566734

Ling Liu, Cong Ling, Yanfei Yan

Publication date: 27 June 2018

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: In this work, an explicit wiretap coding scheme based on polar lattices is proposed to achieve the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel. Firstly, polar lattices are used to construct secrecy-good lattices for the mod-$Lambd{a}_s$ Gaussian wiretap channel. Then we propose an explicit shaping scheme to remove this mod-$Lambd{a}_s$ front end and extend polar lattices to the genuine Gaussian wiretap channel. 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 logN log(logN)). The proposed scheme is proven to be semantically secure.

Full work available at URL: https://arxiv.org/abs/1503.02313

Mathematics Subject Classification ID

Authentication, digital signatures and secret sharing (94A62) Source coding (94A29)

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