Helper-Assisted Coding for Gaussian Wiretap Channels: Deep Learning Meets PhySec

TL;DR

This work tackles secure communication over Gaussian wiretap channels when a helper assists the transmitter, focusing on explicit short-blocklength codes ($n\leq 64$). It introduces a modular two-layer design: a reliability layer realized as a SIC-inspired autoencoder and a security layer built from 2-universal hash functions to bound information leakage $I(S;Z^n)$. The authors validate substantial leakage improvements over point-to-point schemes, extend the approach to multiple helpers and Gaussian MAC-WT scenarios, and propose an alternative AI-based reliability architecture to reduce training time. They also discuss practical considerations, such as leakage estimation with MINE and CLUB, and outline future work on larger blocklengths and fading channels, making the framework a step toward practical, cooperative physical-layer security.

Abstract

Consider the Gaussian wiretap channel, where a transmitter wishes to send a confidential message to a legitimate receiver in the presence of an eavesdropper. It is well known that if the eavesdropper experiences less channel noise than the legitimate receiver, then it is impossible for the transmitter to achieve positive secrecy rates. A known solution to this issue consists in involving a second transmitter, referred to as a helper, to help the first transmitter to achieve security. While such a solution has been studied for the asymptotic blocklength regime and via non-constructive coding schemes, in this paper, for the first time, we design explicit and short blocklength codes using deep learning and cryptographic tools to demonstrate the benefit and practicality of cooperation between two transmitters over the wiretap channel. Specifically, our proposed codes show strict improvement in terms of information leakage compared to existing codes that do not consider a helper. Our code design approach relies on a reliability layer, implemented with an autoencoder architecture based on the successive interference cancellation method, and a security layer implemented with universal hash functions. We also propose an alternative autoencoder architecture that significantly reduces training time by allowing the decoders to independently estimate messages without successively canceling interference by the receiver during training. Additionally, we show that our code design is also applicable to the multiple access wiretap channel with helpers, where two transmitters send confidential messages to the legitimate receiver.

Figures (18)

• Figure 1: Gaussian wiretap channel with a helper.
• Figure 2: Our code design consists of a reliability layer and a security layer. The reliability layer is implemented using two encoders $(e^0_{1,n}, e^0_{2,n})$ and two decoders $(d^0_{1, n}, d^0_{2, n})$, and the security layer is implemented using the functions $\varphi$ and $\psi$.
• Figure 3: Architecture of the autoencoder based on SIC.
• Figure 4: Comparison of schemes based on joint decoding, SIC, and time-sharing when $h_1=1$, $h_2=1$, $n=8$, $P_1=2$, $P_2=2$, and $\sigma^2_Y=6$.
• Figure 5: When $\sigma^2_Y=1$, $\sigma^2_Z=1$, $h_1=1$, $h_2=1$, $(\frac{q_1}{n},\frac{q_2}{n})~\in~\{(\frac{4}{12},\frac{4}{12}), (\frac{6}{16},\frac{6}{16}), (\frac{8}{20},\frac{8}{20}), (\frac{10}{24},\frac{10}{24})\}$, $k_1=1$, $P_1=2$, and $P_2=12$. (a) Average probability of error versus blocklength. (b) Case 1: Information leakage versus blocklength obtained for $g_1=1$ and $g_2=0.3$. (c) Case 2: Information leakage versus blocklength obtained for $g_1=0.2$ and $g_2=0.3$.

Theorems & Definitions (5)

• Definition 1
• Definition 2
• Definition 3
• Definition 4
• Definition 5