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IEEE Malaysia International Conference on Communications (MICC)

A study on quick simulation for estimation of low FER of LDPC codes

Takakazu Sakai, Koji Shibata

Published Dec 1, 2009• 3 citations
Publisher

Abstract

This study shows a new design method of a simulation probability density function (PDF) for a fast frame error rate (FER) evaluation of low-density parity-check (LDPC) codes. It is difficult to evaluate a very low FER of LDPC codes by Monte Carlo simulation methods since it has excellent performance under iterative decoding. Cole et al. proposed a three-step estimation method of the low FER of LDPC codes of moderate block length. By applying the importance sampling method, which is one of the fast simulation methods, the simulation time of the error performance of LDPC codes can be reduced. Another simulation PDF, which can treat more dominant trapping sets (TS) than Cole et al.'s method, is proposed. The selection of the dominant TS as proportional to its probability reduces the number of simulation runs without deteriorating the accuracy of the estimator. Unbiased estimator is given as well as that that of the Cole et al.'s method. Some numerical examples are shown to demonstrate the effectiveness of the proposed method. The simulation time for an LDPC code of length 504 is reduced to 1/10 when we evaluate FER of around 10-14.

DOI
10.1109/micc.2009.5431553

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This study shows a new design method of a simulation probability density function (PDF) for a fast frame error rate (FER) evaluation of low-density parity-check (LDPC) codes. It is difficult to evaluate a very low FER of LDPC codes by Monte Carlo simulation methods since it has excellent performance under iterative decoding. Cole et al. proposed a three-step estimation method of the low FER of LDPC codes of moderate block length. By applying the importance sampling method, which is one of the fast simulation methods, the simulation time of the error performance of LDPC codes can be reduced. Another simulation PDF, which can treat more dominant trapping sets (TS) than Cole et al.'s method, is proposed. The selection of the dominant TS as proportional to its probability reduces the number of simulation runs without deteriorating the accuracy of the estimator. Unbiased estimator is given as well as that that of the Cole et al.'s method. Some numerical examples are shown to demonstrate the effectiveness of the proposed method. The simulation time for an LDPC code of length 504 is reduced to 1/10 when we evaluate FER of around 10-14.
In this paper, we propose an estimation method of a very low bit error rate (HER) of low-density parity-check (LDPC) codes. No analytical tool is available to evaluate performance of LDPC codes, and traditional Monte Carlo simulation methods can not estimate low HER of LDPC codes due to the limitation of time. Cole et al, show a fast frame error rate simulation method of LDPC codes by applying importance sampling (IS). At first, we extend Cole et aI.'s method to the HER estimation of LDPC codes. Since the simulation time of the HER evaluation version of the Cole et aI.'s method is proportional to the number of total dominant trapping sets used in the simulation, we should appropriately choose the dominant trapping sets to reduce the simulation time. To avoid the difficulty, we propose another simulation method, which selects a dominant trapping set as proportional to its upper bound. Additionally, we show some numerical examples to demonstrate the effectiveness of the proposed method. When we evaluate HER of 10−16, the simulation time of the proposed method is reduced to 1/6.6 of that of the HER evaluation version of the Cole et al.'s method under the condition of the same accuracy of the estimator.
This paper shows a fast estimation method of very low error rate of low-density parity-check (LDPC) codes. No analytical tool is available to evaluate performance of LDPC codes, and the traditional Monte Carlo simulation methods can not estimate the low error rate of LDPC codes due to the limitation of time. To conquer this problem, we propose another simulation method which is based on the optimal simulation probability density function (PDF). The proposed simulation PDF can also avoid the dependency between the simulation time and the number of dominant trapping sets, which is the problem of some fast simulation methods based on the error event simulation method. Additionally, we show some numerical examples to demonstrate the effectiveness of the proposed method. The simulation time of the proposed method is reduced to almost less than 1/10 of that of Cole et al.'s method under the condition of the same accuracy of the estimator.
We present an importance sampling method for the evaluation of the low frame error rate (FER) performance of LDPC codes under iterative decoding. It relies on a combinatorial characterization of absorbing sets, which are the dominant cause of decoder failure in the low FER region. The biased density in the importance sampling scheme is a mean-shifted version of the original Gaussian density, which is suitably centered between a codeword and a dominant absorbing set. This choice of biased density yields an unbiased estimator for the FER with a variance lower by several orders of magnitude than the standard Monte Carlo estimator. Using this importance sampling scheme in software, we obtain good agreement with the experimental results obtained from a fast hardware emulator of the decoder.
This paper shows a fast simulation method of low-density parity-check (LDPC) codes over an additive non-Gaussian noise channel. The evaluation of an error performance of LDPC codes is usually executed by using a Monte-Carlo simulation since the theoretical calculation method has not been reported. It is very difficult to evaluate an error performance of LDPC codes with finite block length when the error probability is very low. To solve this problem, some fast simulation methods by using importance sampling (IS) are proposed. However, the conventional methods can not reduce the simulation time of LDPC codes over an additive non-Gaussian noise channel because the simulation probability density function (PDF) used in IS is designed for an additive white Gaussian noise. We propose a new simulation PDF design related to the Chernoff bound to estimate an error performance of LDPC codes over an additive non-Gaussian noise channel. In addition, we show some numerical examples to demonstrate the effectiveness of the proposed simulation method. The simulation time of the proposed method is reduced to about 1/2000 of that of the conventional method when we estimate the frame error rate of 10−10.
This paper shows a fast simulation method of low-density parity-check (LDPC) codes by using importance sampling (IS). In IS, the design of the simulation probability density function (PDF) plays a very important role to reduce the simulation time. We derive the optimal simulation PDF, which can reduce the variance of the estimator to zero. Since the optimal simulation PDF includes true error probability, it can not be utilized in the practical simulation. The simulation PDF which approximates the optimal simulation PDF is proposed. In addition, we show some numerical examples to show the effectiveness of the proposed simulation method.
Abstract — The error-correcting performance of low-density parity check (LDPC) codes, when decoded using practical iterative decoding, is known to approach Shannon limits in the asymptotic limit of large blocklengths. A substantial limitation to the use of finite-length LDPC codes is the presence of an error floor in the low frame error rate (FER) region. This paper develops a method, based on importance sampling and high SNR asymptotics as applied to suitably defined absorbing structures within the LDPC code, to predict error floors. Our results are in very close agreement with hardware-based experimental results, and moreover extend the prediction of the error probability to even lower regions. We compute both importance sampling estimates of error probabilities and deterministic estimates that are guaranteed to lower bound the error probability in the high SNR regime. I.