On the capacity of the Gaussian channel with a finite number of input levels

An analytic confirmation of an observation made by G. Ungerboeck (1965) that approximately optimal performance on a Gaussian channel with capacity C can be obtained with about 2/sup C+1/ levels is given. In particular, the results imply that by using about 2/sup C-1/ levels, a rate of nearly C-1 bit can be achieved, and that by using 2/sup C+1/ levels a rate of about C-0.4 bits can be achieved.<
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