Superposition lattice coding for Gaussian broadcast channel with confidential message

Abstract

In this paper, we propose superposition coding based on the lattice Gaussian distribution to achieve strong secrecy over the Gaussian broadcast channel with one confidential message, with a constant gap to the secrecy capacity (only for the confidential message). The proposed superposition lattice code consists of a lattice Gaussian code for the Gaussian noise and a wiretap lattice code with strong secrecy. The flatness factor is used to analyze the error probability, information leakage and achievable rates. By removing the secrecy coding, we can modify our scheme to achieve the capacity of the Gaussian broadcast channel with one common and one private message without the secrecy constraint.