Even in almost-Gaussian discrete signaling systems, the Gaussian approximation underestimates the true information rate, and for nonlinear continuous systems its accuracy depends on how it is applied.
Any difference between the exact information rate and the Gaussian information rate must then be a result of the Gaussian approximation
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Mutual Information Rate -- Linear Noise Approximation and Exact Computation
Even in almost-Gaussian discrete signaling systems, the Gaussian approximation underestimates the true information rate, and for nonlinear continuous systems its accuracy depends on how it is applied.