Simulation Probability Density Function Design for Turbo Codes

Abstract

We research on an importance sampling (IS) simulation to estimate a low error probability of turbo codes. The simulation time reduction in IS depends on another probability density function (p.d.f.) called simulation p.d.f. The previous IS simulation method can not evaluate the error probability on the low SNR and waterfall region. We derive the optimal simulation p.d.f. which gives the perfect estimator. A new simulation p.d.f. design, which is related to the optimal one, is proposed to overcome the problem of the previous IS method. The proposed IS simulation can evaluate all possible error patterns. Finally, some computer simulations show that the proposed method can evaluate the error probability on the low SNR, waterfall, and error floor regions. At the evaluation of the BER of 10-7, the simulation time of the proposed method is about 1/350 times as short as that of the Monte-Carlo simulation. When the BER is less than 7 × 10-8, the proposed method requires shorter simulation time than the conventional IS method.