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