Minimum-Variance Importance-Sampling Bernoulli Estimator for Fast Simulation of Linear Block Codes over Binary Symmetric Channels

摘要

In this paper the choice of the Bernoulli distribution as biased distributionfor importance sampling (IS) Monte-Carlo (MC) simulation of linear block codesover binary symmetric channels (BSCs) is studied. Based on the analyticalderivation of the optimal IS Bernoulli distribution, with explicit calculationof the variance of the corresponding IS estimator, two novel algorithms forfast-simulation of linear block codes are proposed. For sufficiently highsignal-to-noise ratios (SNRs) one of the proposed algorithm is SNR-invariant,i.e. the IS estimator does not depend on the cross-over probability of thechannel. Also, the proposed algorithms are shown to be suitable for theestimation of the error-correcting capability of the code and the decoder.Finally, the effectiveness of the algorithms is confirmed through simulationresults in comparison to standard Monte Carlo method.