機率研討會
主講者: Professor Kenjiro Yanagi (Yamaguchi University)
講題: Reviews on Capacity of Gaussian Channels with or without Feedback
時間: 2012-09-24 (Mon.)  14:00 - 15:00
地點: 數學所 722 研討室 (台大院區)
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.
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