Importance sampling for LDPC codes based on optimal simulation probability density function

This paper shows a fast simulation method of low-density parity-check (LDPC) codes by using importance sampling (IS). In IS, the design of the simulation probability density function (PDF) plays a very important role to reduce the simulation time. We derive the optimal simulation PDF, which can reduce the variance of the estimator to zero. Since the optimal simulation PDF includes true error probability, it can not be utilized in the practical simulation. The simulation PDF which approximates the optimal simulation PDF is proposed. In addition, we show some numerical examples to show the effectiveness of the proposed simulation method.