Learning End-to-End Codes for the BPSK-constrained Gaussian Wiretap Channel

Finite-length codes are learned for the Gaussian wiretap channel in an end-to-end manner assuming that the communication parties are equipped with deep neural networks (DNNs), and communicate through binary phase-shift keying (BPSK) modulation scheme. The goal is to find codes via DNNs which allow a pair of transmitter and receiver to communicate reliably and securely in the presence of an adversary aiming at decoding the secret messages. Following the information-theoretic secrecy principles, the security is evaluated in terms of mutual information utilizing a deep learning tool called MINE (mutual information neural estimation). System performance is evaluated for different DNN architectures, designed based on the existing secure coding schemes, at the transmitter. Numerical results demonstrate that the legitimate parties can indeed establish a secure transmission in this setting as the learned codes achieve points on almost the boundary of the equivocation region. I. INTRODUCTION Physical layer (PHY) security has been put forth as an alternative/aid to the higher-layer security approaches including cryptography in order to relieve the burden placed by them upon the communication systems in various ways. Wiretap channel [1] is a widely-known theoretical model for studying PHY security from an information-theoretic perspective. The importance of achieving physical layer security for this model through finite alphabet signaling like binary phase-shift keying (BPSK) modulation is highlighted in many works [1], [2]. Several works have studied this channel and designed coding schemes to ensure security for that. Specifically, the authors in [3] have proposed an encoding technique called scrambling which could result in BERs very close to 0.5 for the eavesdropper (Eve) through error propagation, while ensuring a A. Nooraiepour is with WINLAB, Department of Electrical and Computer Engineering, Rutgers University, NJ, USA. S. Rezaei Aghdam is with the Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden (emails: alireza.nooraiepour@rutgers.edu, sinar@chalmers.se).