A wiretap channel is served as the fundamental model of physical layer security techniques, where the secrecy capacity of the Gaussian wiretap channel is proven to be achieved by Gaussian input. However, there remains a gap between the Gaussian secrecy capacity and the secrecy rate with conventional uniformly distributed discrete constellation input, e.g. amplitude shift keying (ASK) and quadrature amplitude modulation (QAM). In this paper, we propose a probabilistic shaped multilevel polar coding scheme to bridge the gap. Specifically, the input distribution optimization problem for maximizing the secrecy rate with ASK/QAM input is solved. Numerical results show that the resulting sub-optimal solution can still approach the Gaussian secrecy capacity. Then, we investigate the polarization of multilevel polar codes for the asymmetric discrete memoryless wiretap channel, and thus propose a multilevel polar coding scheme integration with probabilistic shaping. It is proved that the scheme can achieve the secrecy capacity of the Gaussian wiretap channel with discrete constellation input, and satisfies the reliability condition and weak security condition. A security-oriented polar code construction method to natively satisfies the leakage-based security condition is also investigated. Simulation results show that the proposed scheme achieves more efficient and secure transmission than the uniform constellation input case over both the Gaussian wiretap channel and the Rayleigh fading wiretap channel.

翻译：窃听信道是物理层安全技术的基础模型，其中高斯窃听信道的保密容量已被证明可通过高斯输入实现。然而，高斯保密容量与采用传统均匀分布离散星座输入（如幅移键控（ASK）和正交幅度调制（QAM））所能达到的保密速率之间仍存在差距。本文提出一种概率整形多级极化编码方案以弥合该差距。具体而言，解决了针对ASK/QAM输入最大化保密速率的输入分布优化问题。数值结果表明，所得次优解仍能逼近高斯保密容量。随后，我们研究了非对称离散无记忆窃听信道的多级极化码极化特性，进而提出一种融合概率整形的多级极化编码方案。理论证明该方案能够实现离散星座输入下高斯窃听信道的保密容量，并满足可靠性条件与弱安全条件。本文还探讨了一种本征满足基于泄露安全条件的安全导向极化码构造方法。仿真结果表明，在高斯窃听信道与瑞利衰落窃听信道中，所提方案相比均匀星座输入方案能实现更高效且更安全的传输。