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IEEE Wireless Communications and Networking Conference

A local flat histogram method for evaluating the performance of LDPC codes

Yuan Liu, Weigang Chen

Published Mar 1, 2015• 1 citation
Publisher

Abstract

The performance of low-density parity-check (LDPC) codes can be evaluated by using the dual adaptive importance sampling (DAIS) method. To further accelerate the convergence speed of simulation, an improved method is proposed in which the biased distribution is multiplied with an auxiliary biased function. In this proposed method, samples are limited in the restricted region, where most of the events result in decoding failure, by multiplying the original biased distribution of DAIS method by a second bias. This scheme speeds up the convergence of simulation in the restricted region. Compared with the traditional DAIS method, simulation results for two specific LDPC codes verify that this proposed method achieves the significant simulation gain without sacrificing the accuracy.

DOI
10.1109/wcnc.2015.7127471

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The performance of low-density parity-check (LDPC) codes can be evaluated by using the dual adaptive importance sampling (DAIS) method. To further accelerate the convergence speed of simulation, an improved method is proposed in which the biased distribution is multiplied with an auxiliary biased function. In this proposed method, samples are limited in the restricted region, where most of the events result in decoding failure, by multiplying the original biased distribution of DAIS method by a second bias. This scheme speeds up the convergence of simulation in the restricted region. Compared with the traditional DAIS method, simulation results for two specific LDPC codes verify that this proposed method achieves the significant simulation gain without sacrificing the accuracy.
An improved dual adaptive importance sampling (DAIS) method is proposed to accelerate the simulation of low density parity check (LDPC) codes at high Signal-to-Noise Ratios (SNRs). First, we observed an interesting phenomenon that the conditional probabilities of the error events, which are caused by different noise realizations in the same control quantity bin at the different SNRs, are nearly identical in DAIS. Then, we obtain the joint probabilities of the unconstrained simulations at the high SNRs by substituting the conditional probabilities at the high SNRs with that at the low SNRs based on the observation. This spares the decoding computations of the unconstrained simulation at the high SNRs, and therefore reduces the simulation time. For the specific LDPC code, simulation results verify that the improved method achieves significant simulation gain compared with traditional DAIS, while maintaining the same accuracy.
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.
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.