Derivative of Mutual Information at Zero SNR: The Gaussian-Noise Case
Yihong Wu, Dongning Guo, Sergio Verdú · IEEE Transactions on Information Theory · 2011
Assuming additive Gaussian noise, a general sufficient condition on the input distribution is established to guarantee that the ratio of mutual information to signal-to-noise ratio (SNR) goes to one half nat as SNR vanishes. The result allows SNR-dependent input distribution and side information.