Importance sampling for coded-modulation error probability estimation

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.This work has been funded in part by the European Research Council under ERC grant agreement 725411, and by the Spanish Ministry of Economy and Competitiveness under grant TEC2016-78434-C3-1-R