ON THE CAPACITY OF THE DISCRETE-TIME GAUSSIAN-CHANNEL WITH DELAYED FEEDBACK

We give an upper bound on the finite block length capacity of the discrete-time nonstationary Gaussian channel with delayed feedback. With the aid of minimization of a quadratic form, it is proved that the L time-delayed feedback capacity C-nFB(L)(P) and the nonfeedback capacity C-n(P) satisfy C-n(P) less than or equal to C-nFB(L)(P) less than or equal to C-n(P*) where P* is concretely given. And we give a sufficient condition for C-nFB(L)(P) to be increased by L time-delayed feedback. Finally we also give a necessary and sufficient condition for C-nFB(2)(P) of a class of Gaussian channel to be increased by 2 time-delayed feedback.