Probabilistic Shaped Multilevel Polar Coding for Wiretap Channel

TL;DR

This paper introduces a probabilistic shaped multilevel polar coding scheme that effectively approaches the Gaussian secrecy capacity for wiretap channels using discrete constellations, enhancing secure communication.

Contribution

It proposes a novel probabilistic shaping and multilevel polar coding method that achieves the secrecy capacity with ASK/QAM inputs, bridging the gap with Gaussian inputs.

Findings

Approaches Gaussian secrecy capacity with probabilistic shaping.

Achieves secure transmission over Gaussian and Rayleigh fading wiretap channels.

Provides a security-oriented polar code construction method.

Abstract

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.