Abstract
In this paper, we consider a scalar Gaussian Channel with minimum amplitude constraint, and investigate when the capacity-achieving input is binary. First, we study the case that the input satisfies both minimum and peak amplitude constraints and find that the optimal input is discrete. Then, for a given minimum amplitude, we find sufficient conditions that the peak amplitude constraint must satisfy such that the optimal input is binary and when it is not binary. Similarly, for a given peak amplitude, we find sufficient conditions that the minimum amplitude constraint must satisfy such that the optimal input is binary and when it is not binary. Finally, we find that when the input satisfies minimum amplitude and average power constraints, the optimal input is not binary, regardless of whether there is also a peak amplitude constraint.
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