Maximum entropy and the method of moments in performance of digital communications systems.

Maximum entropy criterion for estimating an unknown probability density function from its moments has been applied to evaluation of average error probability in digital communications. We have developed an interactive program that performs the task efficiently. Accurate averages are obtained, even when a low number of moments are available. The method is very stable and the results compare favorably with corresponding ones from powerful and widely used, Gauss-Quadrature-Rules (GQR) method. For test cases presented in this work, the maximum entropy method achieved results with typically 6 moments while GQR method required 31 moments to obtain the corresponding results, as accurately. This could be very important in those practical problems where only a low number of moments is available. For the same cases GQR method, using only 6 moments, produced inaccurate results.