A Note on Improved Treatment of Gaussian Communication Process

In order to discuss the efficiency of information transmission of the Gaussian communication processes consistently, we introduced an entropy type functional and a mutual entropy type functional in reference [16]. In that study, we used the set of Gaussian input measures with covariance operators of trace one. In this paper, we refine the formulation and modify the entropy type complexity and the mutual entropy type complexity to be able to study the efficiency of information transmission for more general input Gaussian measures and Gaussian channels.