Maximum Entropy and Average Error Rates in Digital Communication Systems

F. Solms
Dept Applied Mathematics
Rand Afrikaans University
PO Box 524
Auckland Park
2092
South Africa

J.S. Kunicki
Cybernetics Laboratory
Rand Afrikaans University
PO Box 524
Auckland Park
2092
South Africa

P.G.W. van Rooyen
Alcatel/Altec/Telkom
PO Box 286
Boksburg
1460
South Africa

Abstract

We show that the Gauss-Quadrature method, which is widely used in performance evaluation of digital communication systems, fails under certain, frequently encountered circumstances and in particular for large values of the signal to noise ratio, i.e. when the subsequent moments grow in absolute size. The maximum entropy method, on the other hand, continues to give reliable results for the average error rates as a function of the signal to noise ratio. Furthermore, when only few moments of the error probability distribution function are known the results obtained via the maximum entropy are far superior to the Gauss-Quadrature results. This is especially significant when the moments are obtained experimentally --- typically only four moments are measured. As one would expect, two moments of a Gaussian error probabilty distribution suffice to give an analysically exact result. Finally, in practice one aims to work with high signal to noise ratios and with low error probabilties. Hence the accuracy of the tail probabilties is important. This is the area where the maximum entropy reuslts give the most improvement on the results obtained via the traditional Gauss-Quadrature method.
MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk