Convergence of mutual information of continuous Gaussian channel under Picard's iteration

Tsz Hin Ng

Published 2017-10-15Version 1

The mutual information between the source message and output signal of a continuous time Gaussian channel is given by a celebrated formula, which is, however, difficult to apply since it involves the solution of a stochastic functional differential equation (SFDE). In this paper, we would like to show the convergence to the quantity by considering the sequence of mutual information between the source message and the Picard's iteration generated in the given SFDE.