This paper proposes an efficient simulation method based on importance sampling to estimate the random-coding error probability of coded modulation. The technique is valid for complex-valued modulations over Gaussian channels, channels with memory, and naturally extends to fading channels. The simulation method is built on two nested importance samplers to respectively estimate the pairwise error probability and generate the channel input and output. The effect of the respective number of samples on the overall bias and variance of the estimate of the error probability is characterized. For a memoryless channel, the estimator is shown to be consistent and with a small variance, growing with the square root of the code length, rather than the exponential growth of a standard Monte Carlo estimator.

中文翻译：

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编码调制误差概率估计的重要性采样

本文提出了一种基于重要性采样的高效仿真方法来估计编码调制的随机编码错误概率。该技术适用于高斯信道、带记忆信道的复值调制，并且自然扩展到衰落信道。仿真方法建立在两个嵌套的重要性采样器上，分别估计成对错误概率并生成通道输入和输出。表征了各个样本数量对错误概率估计的总体偏差和方差的影响。对于无记忆信道，估计量显示为一致且方差很小，随着代码长度的平方根增长，而不是标准蒙特卡罗估计量的指数增长。