Differential Entropy of the Conditional Expectation under Gaussian Noise

This paper considers an additive Gaussian noise channel with arbitrarily distributed finite variance input signals. It studies the differential entropy of the minimum mean-square error (MMSE) estimator and provides a new lower bound which connects the differential entropy of the input, output, and conditional mean. That is, the sum of differential entropies of the conditional mean and output is always greater than or equal to twice the input differential entropy. Various other properties such as upper bounds, asymptotics, Taylor series expansion, and connection to Fisher Information are obtained. An application of the lower bound in the remote-source coding problem is discussed, and extensions of the lower and upper bounds to the vector Gaussian channel are given.

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Toyomu Matsuda

We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in

L_m

of Riemann type sums

\sum _{[s,t] \in \pi } A_{s,t}

for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...

Cambridge Univ Press2024

Differential Entropy of the Conditional Expectation under Gaussian Noise

Spectral Estimators for High-Dimensional Matrix Inference

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Differential Entropy of the Conditional Expectation Under Additive Gaussian Noise

Spectral Estimators for High-Dimensional Matrix Inference

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Differential Entropy of the Conditional Expectation Under Additive Gaussian Noise