Multilevel coding for peak power limited complex Gaussian channels

For transmission over the peak power limited complex Gaussian channel with various rates, the semi-continuous transmitter probability density function (pdf) maximizing mutual information is approximated by discrete equiprobable signal points. Since there is no need for shaping, in most cases only one bit of redundancy per two dimensions is sufficient to come very close to capacity. These results are in contrast to the average power limited channel requiring two bits of redundancy for coding and shaping. Combinations of properly designed multilevel coding (MLC) schemes with these discrete signal sets show a trade-off between bandwidth efficiency and peak power similar to the case of average power limitation.