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papersTODAY 04:00 UTC

Paper Links Zero-SNR Analyticity of Scalar MMSE to Gaussian Inputs

The paper studies a scalar channel where a real random variable X is observed under additive standard Gaussian noise scaled by the square root of a signal-to-noise parameter. Assuming a square-exponential moment condition on X, the author shows that the minimum mean-square error behaves analytically near zero SNR only when X is Gaussian, making that property equivalent to Gaussianity of the input. The result gives a way to detect non-Gaussian structure from the low-SNR behavior of the MMSE curve.

Gaussian distribution information theory minimum mean-square error scalar channel signal-to-noise ratio zero-SNR analyticity

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arXiv cs.LGZero-SNR Analyticity of the Scalar MMSE Is Equivalent to Gaussianity ↗TODAY 04:00 UTC