Optimum discrete signaling over channels with arbitrary noise distribution


R. Mathar, A. Schmeink, M. Zivkovic,


        General channels with arbitrary noise distributions and a finite set of signaling points are considered in this paper. We aim at finding the capacity-achieving input distribution. As a structural result we first demonstrate that mutual information is a concave function of the input distribution and a convex function of the channel transfer densities. Using the Karush-Kuhn-Tucker theory, capacity achieving distributions are then characterized by constant Kullback-Leibler divergence between each channel transfer density and the mixture hereof built by using the probabilities as weights. If, as a special case, the noise distribution and the signaling points are rotationally symmetric, then the uniform input distribution is optimal. For 2-PAM modulation and certain types of asymmetric noise distributions, including exponential, gamma and Rayleigh, we present extensive numerical evaluations of the optimal input. Furthermore, for 4-QAM we determine the optimal input from a restricted symmetric class of distributions for correlated Gaussian noise.

BibTEX Reference Entry 

	author = {Rudolf Mathar and Anke Schmeink and Milan Zivkovic},
	title = "Optimum discrete signaling over channels with arbitrary noise distribution",
	booktitle = "2nd International Conference on Signal Processing and Communication Systems (ICSPCS) ",
	address = {Gold Coast, Australia},
	month = Dec,
	year = 2008,


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