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International Conference on Communications

An IS Simulation Technique for Very Low BER Performance Evaluation of LDPC Codes

Enver Çavuş, Charles L. Haymes, Babak Daneshrad

Published Jun 1, 2006• 23 citations
Publisher

Abstract

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.

DOI
10.1109/icc.2006.254893

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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.

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Ronald Holzlöhner, Amitkumar Mahadevan, Curtis R. Menyuk +2 more

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IEEE Communications Letters•Jan 31, 2005•58 citations
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 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.
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.
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.
Low-density parity-check (LDPC) codes have shown capacity-approaching performance with soft iterative decoding algorithms. Simulating LDPC codes at very low error rates normally takes an unacceptably long time. We consider importance sampling (IS) schemes for the error rate estimation of LDPC codes, with the goal of dramatically reducing the necessary simulation time. In IS simulations, the sample distribution is biased to emphasize the occurrence of error events and efficiency can be achieved with properly biased sample distributions. For LDPC codes, we propose an IS scheme that overcomes a difficulty in traditional IS designs that require codebook information. This scheme is capable of estimating both codeword and bit error rates. As an example, IS gains on the order of 105 are observed at a bit error rate (BER) of 10-15 for a (96, 48) code. We also present an importance sampling scheme for the decoding of loop-free multiple-layer trees. This scheme is asymptotically efficient in that, for an arbitrary tree and a given estimation precision, the required number of simulations is inversely proportional to the noise standard deviation. The motivation of this study is to shed light on an asymptotically efficient IS design for LDPC code simulations. For an example depth-3 regular tree, we show that only 2400 simulation runs are needed to achieve a 10% estimation precision at a BER of 10-75. Similar promising results are also shown for a length-9 rate-1/3 regular code after being converted to a decoding tree. Finally, we consider a convolutionally coded CDMA system with iterative multiuser detection and decoding. In contrast to previous work in this area, a differential encoder is inserted to effect an interleaver gain. We view the CDMA channel as a periodically time-varying ISI channel. The receiver jointly decodes the differential encoders and the CDMA channel with a combined trellis, and shares soft output information with the convolutional decoders in an iterative (turbo) fashion. Dramatic gains over conventional convolutionally coded systems are demonstrated via simulation. We also show that there exists an optimal code rate under a bandwidth constraint. The performance and optimal code rates are also demonstrated via density evolution analysis.