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IEEE Communications Letters

Evaluation of the very low BER of FEC codes using dual adaptive importance sampling

Ronald Holzlöhner, Amitkumar Mahadevan, Curtis R. Menyuk, Joel M. Morris, John W. Zweck

Published Jan 31, 2005• 58 citations
Publisher

Abstract

We evaluate the error-correcting performance of a low-density parity-check (LDPC) code in an AWGN channel using a novel dual adaptive importance sampling (DAIS) technique based on multicanonical Monte Carlo (MMC) simulations, that allows us to calculate bit error rates as low as 10/sup -19/ for a (96,50) LDPC code without a priori knowledge of how to bias. Our results agree very well with standard MC simulations, as well as the union bound for the code.

DOI
10.1109/lcomm.2005.02012

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We evaluate the error-correcting performance of a low-density parity-check (LDPC) code in an AWGN channel using a novel dual adaptive importance sampling (DAIS) technique based on multicanonical Monte Carlo (MMC) simulations, that allows us to calculate bit error rates as low as 10/sup -19/ for a (96,50) LDPC code without a priori knowledge of how to bias. Our results agree very well with standard MC simulations, as well as the union bound for the code.
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.
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.