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IET Communications

Performance evaluation of irregular low-density parity-check codes at high signal-to-noise ratio

X. Zheng, Francis C. M. Lau, Chi Kong Tse

Published Jul 22, 2011• 7 citations
Publisher

Abstract

Elementary trapping sets (ETSs) have been found to be the main cause of error floor in the decoding of low-density parity-check (LDPC) codes. Moreover, irregular LDPC codes that avoid harmful [w; u; e] ETSs have been constructed and have shown to possess superior error performance compared with other LDPC codes. In this paper, we attempt to evaluate irregular LDPC code performance under an additive white Gaussian noise channel within the high SNR region using the importance sampling (IS) approach in conjunction with the identification of [w; u; e] ETSs. For any given irregular LDPC code, we will first apply a three-step method that aims to search as many ETSs within the code as possible. Then, we will classify these ETSs into different groups based on their labels, i.e., [w; u; e]'s. Further, by dividing the error region into various sub-regions centered by ETSs, we apply the IS simulator to evaluate the error rate of each of the sub-regions. Based on the error rates of all the sub-regions, we can estimate the overall error rate of the LDPC code. Results have indicated that our proposed IS scheme can produce speed-up gains up to 3.9×109 times compared to Monte Carlo simulations.

DOI
10.1049/iet-com.2010.0741

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Elementary trapping sets (ETSs) have been found to be the main cause of error floor in the decoding of low-density parity-check (LDPC) codes. Moreover, irregular LDPC codes that avoid harmful [w; u; e] ETSs have been constructed and have shown to possess superior error performance compared with other LDPC codes. In this paper, we attempt to evaluate irregular LDPC code performance under an additive white Gaussian noise channel within the high SNR region using the importance sampling (IS) approach in conjunction with the identification of [w; u; e] ETSs. For any given irregular LDPC code, we will first apply a three-step method that aims to search as many ETSs within the code as possible. Then, we will classify these ETSs into different groups based on their labels, i.e., [w; u; e]'s. Further, by dividing the error region into various sub-regions centered by ETSs, we apply the IS simulator to evaluate the error rate of each of the sub-regions. Based on the error rates of all the sub-regions, we can estimate the overall error rate of the LDPC code. Results have indicated that our proposed IS scheme can produce speed-up gains up to 3.9×109 times compared to Monte Carlo simulations.
We introduce an Importance Sampling (IS) method that successfully simulates the performance of Low density Parity Check (LDPC) Codes in an AWGN channel at very low bit error rates (BERs). By effectively finding and biasing bit node combinations that are the dominant sources of error events, called trapping sets, the developed technique provokes more frequent decoder failures. Consequently, fewer simulation runs and higher simulation gains are achieved. Regardless of the block size of an LDPC code, only a few dominant trapping set classes cause decoder failures at low BER regions. Therefore, the proposed technique allows the performance evaluation for any size LDPC code at very low BER regions with remarkable simulation gains. For BERs of 10-20, we observed simulation gains on the order of 1014.
In this paper we propose a novel importance sampling (IS) scheme to estimate the low error-rate performance of low-density parity-check (LDPC) codes over Rayleigh fading channels. The proposed scheme exploits the structural weakness of LDPC codes due to trapping sets (TSs). The Rayleigh fading distribution on the bits belonging to a TS is biased by parameter scaling (PS), while the noise distribution on them is biased via mean translation (MT) according to their fading coefficients. The biases in PS and MT are determined so that the variance of the proposed IS estimator is minimized. The proposed IS scheme is compared with the Monte Carlo (MC) simulator and other IS schemes modified from the conventional IS scheme employed for performance estimation of LDPC codes over an AWGN channel. Numerical results show that it provides much more accurate performance than other IS schemes. Furthermore, the proposed IS estimator is even more efficient than the MC estimator and other IS estimators from the viewpoint of the number of required simulation runs.
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.
The error-correcting performance of low-density parity check (LDPC) codes, when decoded using practical iterative decoding algorithms, is known to be close to Shannon limits for codes with suitably 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 deterministic method of predicting error floors, based on high signal-to-noise ratio (SNR) asymptotics, applied to absorbing sets within structured LDPC codes. The approach is illustrated using a class of array-based LDPC codes, taken as exemplars of high-performance structured LDPC codes. The results are in very good agreement with a stochastic method based on importance sampling which, in turn, matches the hardware-based experimental results. The importance sampling scheme uses a mean-shifted version of the original Gaussian density, appropriately centered between a codeword and a dominant absorbing set, to produce an unbiased estimator of the FER with substantial computational savings over a standard Monte Carlo estimator. Our deterministic estimates are guaranteed to be a lower bound to the error probability in the high SNR regime, and extend the prediction of the error probability to as low as 10-30. By adopting a channel-independent viewpoint, the usefulness of these results is demonstrated for both the standard Gaussian channel and a channel with mixture noise.