The capacity of the Gaussian channel with feedback

In this paper we provide a rigorous proof that feedback cannot increase the capacity of the channel with additive colored gaussian noise by more than a factor of two. We also give a tighter bound showing that any increase in capacity is less than the normalized correlation between the signal and noise. It is further shown that gaussian signals and linear feedback processing will achieve capacity. The practical implications are that (i) feedback should be used to simplify encoding and decoding since there is little to be gained in the way of increased capacity and (ii) the various proposed schemes which use linear feedback are doing the correct thing.