Define Channel Capacity C Max p(X}1(X;Y) Example(AWGn Channel) p(yx)=(22)exp(1/2a2)(y-x) (X; Y)=H(Y-H(YX) H(Y-p(x) p(ylx)log pyx) dy dx H(Y)-log(2Toe 1/2 The only way to maximize I(X; Y)is to maximize HY) This requires y being normal variable with zero mean Due to Y=X+N, it requires X being a normal variable with zero meanChannel Capacity C = I(X; Y) Max Define {p(X)} Example (AWGN Channel): p(y|x) =(2ps ) exp[-(1/2s ) (y-x) ] = H(Y) - p(x) p(y|x) log p(y|x) dy dx 2 = H(Y) - log (2ps e) I(X; Y) = H(Y) - H(Y|X) The only way to maximize I(X; Y) is to maximize H(Y). This requires Y being normal variable with zero mean. Due to Y = X+N, it requires X being a normal variable with zero mean. -1/2 2 2 - - 2 1/2