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

Takakazu SAKAI; Haruo OGIWARA

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

Takakazu SAKAI, Haruo OGIWARA

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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.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.9 pp.1361-1370

Publication Date: 1996/09/25

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Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)

Category: Coded Modulation

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Takakazu SAKAI, Haruo OGIWARA, "Quick Simulation Method for TCM Scheme Using Importance Sampling without Truncation Error" in IEICE TRANSACTIONS on Fundamentals, vol. E79-A, no. 9, pp. 1361-1370, September 1996, doi: .
Abstract: 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.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/e79-a_9_1361/_p

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@ARTICLE{e79-a_9_1361,
author={Takakazu SAKAI, Haruo OGIWARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Quick Simulation Method for TCM Scheme Using Importance Sampling without Truncation Error},
year={1996},
volume={E79-A},
number={9},
pages={1361-1370},
abstract={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.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Quick Simulation Method for TCM Scheme Using Importance Sampling without Truncation Error
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1361
EP - 1370
AU - Takakazu SAKAI
AU - Haruo OGIWARA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1996
AB - 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.
ER -