Radius Domain-Based Importance Sampling Estimator for Linear Block Codes over the AWGN Channel

In this paper, the problem of efficiently evaluating the error performance of linear block codes over the AWGN channel is considered. Based on the geometric structure of the channel, we define the l(2)-norm of the noise vector as a random variable and refer to its sample space as the radius domain. A minimum-variance importance sampling (IS) estimator is proposed by deriving the optimal IS distribution on the radius domain. The IS gain of the proposed estimator compared to the Monte Carlo method is analyzed. The asymptotic IS gain for high SNR, which only depends on the minimum distance of the code, is derived. Finally, the effectiveness of the proposed estimator and the accuracy of the asymptotic IS gain are verified through simulation.