Derivative of Mutual Information at Zero SNR: The Gaussian-Noise Case

Abstract

Abstract-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.Index Terms-Gaussian noise, low-power regime, minimum mean-square error (MMSE), mutual information, signal-to-noise ratio (SNR).

A Practical Consideration on Convex Mutual Information

“…Hence, we utilize a repeated transmission method to improve the lowest level. Because that MI of every level is approximately in straight line at low SNR [7], the negative effect of the repetition is small.…”

A View of Information-Estimation Relations in Gaussian Networks

“…Next, we select the parameters [N 1 , N 2 , δ 1 , δ 2 ] to optimize the region in (110). For simplicity, we focus only on the very strong interference regime (α ≥ 2).…”

“…Wu et al [110] have shown precisely and rigorously, using basic inequalities, that the I-MMSE relationship holds for any input of finite variance. The approach in [110] followed by examining the truncated input.…”

“…The approach in [110] followed by examining the truncated input. Although this approach extends directly for any finite n it is not trivial to extend it to the limit as n → ∞.…”

“…Now, instead of considering the lower bound on the normalized conditional mutual information as done in [110] going through the truncation argument, we examine the I-MMSE relationship directly:…”