K_ε(A) scales as Θ(A √log A) for ε = A^{-β} (β ≥ 1) and between A √log A and A^{3/2} for exponentially small ε, via approximation theory and χ²-divergence control.
An information theoretical identity and a problem involving capacity,
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Support Size of $\varepsilon$-Capacity-Achieving Inputs for the Amplitude-Constrained AWGN Channel
K_ε(A) scales as Θ(A √log A) for ε = A^{-β} (β ≥ 1) and between A √log A and A^{3/2} for exponentially small ε, via approximation theory and χ²-divergence control.