This paper addresses the problem of the Monte Carlo method complexity reduction regarding bit error probability (BEP) estimation. A kernel-based BEP estimator is designed for coded M-ary quadrature amplitude modulation (QAM) transmissions schemes. The design of the kernel estimator is made in a context where the soft observations are spread along a bounded support. An Epanechnikov kernel function is chosen. The optimal smoothing parameter is selected based on an asymptotic mean integrated squared error criterion and replacing the unkonwn density function by a reference distribution. Simulations are run for 4-QAM transmission scheme over a frequency-selective Rayleigh fading channel. The proposed estimator is demonstrated reliable and efficient bringing otherwise significative sample size savings.