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There are rising scenarios in communication systems, where the noises exhibitimpulsive behavior and are not adequate to be modeled as the Gaussiandistribution. The generalized Gaussian distribution instead is an effectivemodel to describe real-world systems with impulsive noises. In this paper, theproblem of efficiently evaluating the error performance of linear block codesover an additive white generalized Gaussian noise (AWGGN) channel isconsidered. The Monte Carlo (MC) simulation is a widely used but inefficientperformance evaluation method, especially in the low error probability regime.As a variance-reduction technique, importance sampling (IS) can significantlyreduce the sample size needed for reliable estimation based on a well-designedIS distribution. By deriving the optimal IS distribution on the one-dimensionalspace mapped from the observation space, we present a general framework todesigning IS estimators for memoryless continuous channels. Specifically, forthe AWGGN channel, we propose an $L_p$-norm-based minimum-variance ISestimator. As an efficiency measure, the asymptotic IS gain of the proposedestimator is derived in a multiple integral form as the signal-to-noise ratiotends to infinity. Specifically, for the Laplace and Gaussian noises, the gainscan be derived in a one-dimensional integral form, which makes the numericalcalculation affordable. In addition, by limiting the use of the union bound toan optimized $L_1$-norm sphere, we derive the sphere bound for the additivewhite Laplace noise channel. Simulation results verify the accuracy of thederived IS gain in predicting the efficiency of the proposed IS estimator.

Fast Performance Evaluation of Linear Block Codes over Memoryless Continuous Channels