Achievable Rates for Two-Way Wire-Tap Channels

We consider two-way wire-tap channels, where two users are communicating with each other in the presence of an eavesdropper, who has access to the communications through a multiple-access channel. We find achievable rates for two different scenarios, the Gaussian two-way wire-tap channel, (GTW-WT), and the binary additive two-way wire-tap channel, (BATW-WT). It is shown that the two-way channels inherently provide a unique advantage for wire-tapped scenarios, as the users know their own transmitted signals and in effect help encrypt the other user’s messages, similar to a one-time pad. We compare the achievable rates to that of the Gaussian multiple-access wire-tap channel (GMAC-WT) to illustrate this advantage.

💡 Research Summary

This paper investigates the secrecy capacity of two-way wire‑tap channels, where two legitimate users exchange messages while an external eavesdropper observes a multiple‑access combination of their signals. Two concrete channel models are studied: the Gaussian Two‑Way Wire‑Tap channel (GTW‑WT) and the Binary Additive Two‑Way Wire‑Tap channel (BATW‑WT). The key insight is that in a two‑way setting each user knows exactly what it transmitted, allowing the receiver to subtract its own signal and recover only the partner’s message. This “self‑knowledge” acts like a one‑time‑pad, dramatically reducing the information that the eavesdropper can glean compared with the traditional Gaussian Multiple‑Access Wire‑Tap (GMAC‑WT) scenario.

The secrecy constraint follows Wyner’s formulation: the normalized conditional entropy H(W|Z)/H(W) must approach one, meaning the eavesdropper learns essentially no information about the secret messages. An (R₁,R₂) pair is declared achievable if, for any ε>0, there exists a code of length n with error probability ≤ε and secrecy leakage ≤ε.

For GTW‑WT the received signals after standard normalization are
Y₁ = √α₁ X₁ + X₂ + N₁,
Y₂ = X₁ + √α₂ X₂ + N₂,
Z = h₁ X₁ + h₂ X₂ + N_W,
with power constraints 0 ≤ P_k ≤ P̄_k. The achievable secrecy region (Theorem 1) is:

R_k ≤ g(P_k) (k=1,2)
R₁+R₂ ≤