Quick Simulation Method for TCM Scheme Using Importance Sampling without Truncation Error

Takakazu SAKAI  Haruo OGIWARA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.9   pp.1361-1370
Publication Date: 1996/09/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coded Modulation
Keyword: 
importance sampling,  Monte-Carlo simulation,  trellis coding,  coded modulation,  non-Gaussian noise,  

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Summary: 
The evaluation of a error probability of a trellis-coded modulation scheme by an ordinary Monte-Carlo simulation method is almost impossible since the excessive simulation time is required to evaluate it. The reduction of the number of simulation runs required is achieved by an importance sampling method, which is one of the variance reduction simulation methods. The reduction of it is attained by the modification of the probability density function, which makes errors more frequent. The error event simulation method, which evaluates the error probability of finite important error events, cannot avoid a truncation error. It is the fatal problem to evaluate the precision of the simulation result. The reason of it is how to design the simulation probability density function. We propose a evaluation method and the design methods of the simulation conditional probability density function. The proposed method simulates any error event starting at the fixed time, and the estimator of it has not the truncation error. The proposed design method approximate the optimum simulation conditional probability density function. By using the proposed method for an additive non-Gaussian noise case, the simulation time of the most effective case of the proposed method is less than 1/5600 of the ordinary Monte-Carlo method at the bit error rate of 10-6 under the condition of the same accuracy if the overhead of the selection of the error events is excluded. The simulation time of the same bit error rate is about 1/96 even if we take the overhead for the importance sampling method into account.