Refinements of the half-bit and factor-of-two bounds for capacity in Gaussian channel with feedback

We consider the upper bounds of the finite blocklength capacity C/sub n,FB/(P) of the discrete time Gaussian channel with feedback. We also let C/sub n/(p) be the nonfeedback capacity. We prove the relations C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/C/sub n/(/spl alpha/P)+ 1/2 ln(1+1//spl alpha/) and C/sub n/(P)/spl les/C/sub n,FB/(P)/spl les/(1+1//spl alpha/)C/sub n/(/spl alpha/P) for any P>0 and any /spl alpha/>0, which induce the half-bit and factor-of-two bounds given by Cover and Pombra (1989) in the special case of /spl alpha/=1.