Fast Simulation of Convolutionally Coded Communication System for Performance Evaluation with A Novel Noise Gauging Method

To estimate the probability Pe of an error event to an accuracy in variance not exceeding \in 2}P_e2, conventional Monte Carlo (MC) requires approximately 1/(2Pe) simulation runs. Hence the low error probabilities demanded for ultra-reliable communication pose a significant issue in simulation-based evaluation of transmission performance. Advanced fast simulation techniques are therefore coveted. Conceptually, we may view a sequence of symbols transmitted by a communication system as a point in a multidimensional space. Channel distortion and noise may cause displacement of the point. The receiver commits an error if it fails to recover the transmitted point location from the received. The efficiency of a simulator depends on how sharply it can differentiate error-causing and non-error-causing displacements and how simply it can determine the probability of encountering an error-causing displacement. We consider convolutionally coded communication in which the receiver employs Viterbi decoding. We propose a corresponding noise gauging function (NGF) which can make relatively sharp differentiation between error-causing and non-error-causing noise vectors. We also propose a way to estimate the distribution of the NGF values to support error rate evaluation. The result is employed in an MC-type technique that adaptively shapes the histogram of the NGF values of the generated noise vector samples towards one that minimizes the variance in Pe estimation under given number of simulation runs. Simulation considering the additive white Gaussian noise channel shows an approximately one to two orders of magnitude in speed-up compared to conventional MC.