Secrecy Capacity of the Gaussian Wire-Tap Channel with Finite Complex Constellation Input

TL;DR

This paper investigates the secrecy capacity of Gaussian wire-tap channels with finite complex constellations, revealing that the capacity curve has a maximum at a certain SNR, unlike the monotonic increase seen with Gaussian inputs.

Contribution

It demonstrates that finite constellations produce a secrecy capacity curve with a single maximum, contrasting with the known behavior for Gaussian codebook inputs.

Findings

Secrecy capacity curves for finite constellations have a single maximum.

Maximum secrecy capacity occurs at a specific SNR for finite constellations.

Simulation results for BPSK, 4-QAM, 16-QAM, and 8-PSK confirm the behavior.

Abstract

The secrecy capacity of a discrete memoryless Gaussian Wire-Tap Channel when the input is from a finite complex constellation is studied. It is shown that the secrecy capacity curves of a finite constellation plotted against the SNR, for a fixed noise variance of the eavesdropper's channel has a global maximum at an internal point. This is in contrast to what is known in the case of Gaussian codebook input where the secrecy capacity curve is a bounded, monotonically increasing function of SNR. Secrecy capacity curves for some well known constellations like BPSK, 4-QAM, 16-QAM and 8-PSK are plotted and the SNR at which the maximum occurs is found through simulation. It is conjectured that the secrecy capacity curves for finite constellations have a single maximum.