Deep Learning for the Gaussian Wiretap Channel

End-to-end learning of communication systems with neural networks and particularly autoencoders is an emerging research direction which gained popularity in the last year. In this approach, neural networks learn to simultaneously optimize encoding and decoding functions to establish reliable message transmission. In this paper, this line of thinking is extended to communication scenarios in which an eavesdropper must further be kept ignorant about the communication. The secrecy of the transmission is achieved by utilizing a modified secure loss function based on cross-entropy which can be implemented with state-of-the-art machine-learning libraries. This secure loss function approach is applied in a Gaussian wiretap channel setup, for which it is shown that the neural network learns a trade-off between reliable communication and information secrecy by clustering learned constellations. As a result, an eavesdropper with higher noise cannot distinguish between the symbols anymore.

I. Introduction

Communication theory addresses the problem of reliably transmitting information and data from one point to another. A communication system itself can be abstracted into three blocks: (1) An encoder at the transmitter side, which takes a message to transmit and encodes it into a codeword. (2) A noisy channel, which transforms the transmitted codeword in a certain way. And (3) a decoder at the receiver side, which estimates the transmitted message based on its noisy channel output. The channel is usually fixed and accounts for example for signal impairments and imperfections in real life scenarios, such as wireless communication. The communication channel of interest in this work is the additive white Gaussian noise channel (AWGN). The aim is now to develop appropriate encoding and decoding schemes to combat the impairments of this channel. This usually involves adding redundancy and introducing sophisticated techniques which use the available communication dimensions (e.g. frequency and time) in an optimal way. However, constructing capacity-achieving coding schemes is a highly non-trivial task even for very simple communication scenarios. It is therefore natural to search for solutions which can simplify this process, for example using deep learning.