Amplitude Constrained Vector Gaussian Wiretap Channel: Properties of the Secrecy-Capacity-Achieving Input Distribution
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This paper studies secrecy-capacity of an n-dimensional Gaussian wiretap channel under a peak-power constraint. This work determines the largest peak-power constraint 𝖱̅_n such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the low amplitude regime. The asymptotic of 𝖱̅_n as n goes to infinity is completely characterized as a function of noise variance at both receivers. Moreover, the secrecy-capacity is also characterized in a form amenable for computation. Several numerical examples are provided, such as the example of the secrecy-capacity-achieving distribution beyond the low amplitude regime. Furthermore, for the scalar case (n=1) we show that the secrecy-capacity-achieving input distribution is discrete with finitely many points at most of the order of 𝖱^2/σ_1^2, where σ_1^2 is the variance of the Gaussian noise over the legitimate channel.
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