  There are rising scenarios in communication systems, where the noises exhibit
impulsive behavior and are not adequate to be modeled as the Gaussian
distribution. The generalized Gaussian distribution instead is an effective
model to describe real-world systems with impulsive noises. In this paper, the
problem of efficiently evaluating the error performance of linear block codes
over an additive white generalized Gaussian noise (AWGGN) channel is
considered. The Monte Carlo (MC) simulation is a widely used but inefficient
performance evaluation method, especially in the low error probability regime.
As a variance-reduction technique, importance sampling (IS) can significantly
reduce the sample size needed for reliable estimation based on a well-designed
IS distribution. By deriving the optimal IS distribution on the one-dimensional
space mapped from the observation space, we present a general framework to
designing IS estimators for memoryless continuous channels. Specifically, for
the AWGGN channel, we propose an $L_p$-norm-based minimum-variance IS
estimator. As an efficiency measure, the asymptotic IS gain of the proposed
estimator is derived in a multiple integral form as the signal-to-noise ratio
tends to infinity. Specifically, for the Laplace and Gaussian noises, the gains
can be derived in a one-dimensional integral form, which makes the numerical
calculation affordable. In addition, by limiting the use of the union bound to
an optimized $L_1$-norm sphere, we derive the sphere bound for the additive
white Laplace noise channel. Simulation results verify the accuracy of the
derived IS gain in predicting the efficiency of the proposed IS estimator.
