The Cutoff Rate of Time Correlated Fading Channels

XI)) and (I(X1; Y 1 Xz ), I( X2; I')), are in Cllm. By symmetry, it is sufficient to show that (I(X1: I' 1 X2), This basically involves finding, for any inputs SI, -1-2 and their output I', a sequence of Xr,X; such that ~z-~I(X;,:I~") and 7i-'I(X;: I,,) tend to I(X1; I' 1 Xz) and I(X2: I,), respectively. The sequences X; and A-; will be chosen as follows: X; is the nth product of X1 and X; is uniform on an (11. M3 f) code for the memoryless channel with transition probability I(X2;Y)) E Cl"