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The authors show that the Gauss-quadrature rule (GQR) method, which is widely used in performance evaluation of digital communication systems, fails under certain frequently encountered conditions. The maximum entropy method (MEM), on the other hand, continues to give reliable results for most of these problems. In cases where the MEM becomes numerically unstable before it achieves sufficient accuracy the authors incorporate a prior estimate of the error probability distribution function (PDF) in the minimum relative entropy (MREM) algorithm in order to improve on the accuracy of their results. They compare the MEM and MREM results to those obtained with the GQR method for AWGN channels with single Rayleigh-path-faded BPSK signals to the P-branch diversity systems. In both cases the GQR method fails for large values of the SNR,