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

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