4 problems

Optimality conjecture for the proposed RIE. The proposed RIE and its associated algorithm are optimal. Here optimality is understood in the general RIE class, where the minimum ach…

Let $Z_n$ be the one-step estimator considered in the paper for the Cauchy parameter $\theta \in \mathbb{H}$, where $\mathbb{H}$ is the upper half-plane, and let $E$ denote expecta…

Let $X$ be an input random variable with any distribution having finite power, and consider the couplings of the Gaussian channel described in the preceding sections, each inducing…

Let $X$ and $Z$ be zero-mean random variables, and for $\rho\in[0,\infty)$ let ${\mathsf{mmse}}(X,\rho)$ denote the minimum mean-square error in estimating $X$ from a Gaussian-nois…