On the Capacity Achieving Input of Amplitude Constrained Vector Gaussian Wiretap Channel

02/01/2022

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by   Antonino Favano, et al.

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This paper studies secrecy-capacity of an n-dimensional Gaussian wiretap channel under the 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 small-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. Furthermore, several numerical examples are provided, such as the example of the secrecy-capacity achieving distribution outside of the small amplitude regime.