Speaker : Professor Kenjiro Yanagi (Yamaguchi University)
Title : Reviews on Capacity of Gaussian Channels with or without Feedback
Time : 2012-09-24 (Mon) 14:00 - 15:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: Let (X,X), (Y,Y) be measurable spaces representing input space and output space, respectively. For x∈X, B∈Y we define ν(x,B) as follows. (1) For any x∈X, ν(x,B ) is probability measure on (Y,Y). (2) For any B∈Y, ν(x,B) is measurable function on (X,X). Then a triple [X,ν,Y ] is called an information channel. Letμ_X be a probability measure on (X,X) representing an input source. We define the following probability measureμ_Y on (Y,Y) as follows. μ_Y (B) =∫ν(x;B) dμ_X(x), B∈Y, μ_Y is called an output source. And we define the following probability measureμ_XY on (X ×Y;X × Y) by μ_XY (C) =∫ν_(x;Cx) dμ_X(x); C∈X×Y; where Cx = {y∈Y;(x, y) ∈C}. In this talk we will consider a Gaussian channel, where X; Y are real separable Banach spaces and for each x∈X,ν(x; B) is a Gaussian measure on (Y; Y). We state several properties of capacity of Gaussian channel without feedback. And also we state a discrete time Gaussian channel with feedback and give some properties about its capacity.