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

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 ${\overline {\text{R}} _n}$ such that an input distribution uniformly distributed on a single sphere is optimal; this regime is termed the low amplitude regime. The asymptotic of ${\overline {\text{R}} _n}$ 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 low amplitude regime.