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Noise Adaptive LDPC Decoding Using Expectation Propagation

Shuang Wang, Lijuan Cui, Samuel S. M. Cheng

Published Dec 1, 2011• 3 citations
Publisher

Abstract

Belief propagation (BP) is a powerful algorithm to decode low- density parity check (LDPC) codes over additive white Gaussian noise (AWGN) channels. However, the traditional BP algorithm cannot adapt efficiently to the statistical change of SNR in an AWGN channel. This paper proposes an adaptive scheme that incorporates expectation propagation (EP) into the BP based LDPC decoding process. The proposed scheme is able to perform online estimation of both stationary and time-varying SNR at the bit-level, and enhance the BP decoding performance simultaneously. Moreover, the proposed EP estimator shows a very fast convergence speed, and the additional computational overhead of the proposed decoder is less than 10% of the standard BP decoder.

DOI
10.1109/glocom.2011.6133838

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Belief propagation (BP) is a powerful algorithm to decode low- density parity check (LDPC) codes over additive white Gaussian noise (AWGN) channels. However, the traditional BP algorithm cannot adapt efficiently to the statistical change of SNR in an AWGN channel. This paper proposes an adaptive scheme that incorporates expectation propagation (EP) into the BP based LDPC decoding process. The proposed scheme is able to perform online estimation of both stationary and time-varying SNR at the bit-level, and enhance the BP decoding performance simultaneously. Moreover, the proposed EP estimator shows a very fast convergence speed, and the additional computational overhead of the proposed decoder is less than 10% of the standard BP decoder.
Belief propagation (BP) is a powerful algorithm to decode low-density parity check (LDPC) codes over additive white Gaussian noise (AWGN) channels. However, the traditional BP algorithm cannot adapt efficiently to the statistical change of SNR in an AWGN channel. This paper proposes an adaptive scheme that incorporates a particle filtering (PF) algorithm into the BP based LDPC decoding process. The proposed scheme is capable to perform online estimation of time-varying SNR at the bit-level and enhance the BP decoding performance simultaneously.
Belief propagation (BP) is a powerful algorithm to decode the low-density parity check (LDPC) codes over the additive white Gaussian noise (AWGN) channel. The traditional BP algorithm cannot adapt efficiently to the statistical change of the AWGN channel. Particle filter is a algorithm to estimate a variable of interest as it evolves over time. In this paper, we use particle filter to estimate the noise power and feed back to the BP algorithm in real time. We found that compared with the traditional BP algorithm with fixed estimated noise power, BP algorithm based on particle filter not only give a good real-time estimate for the channel noise, but also achieve a lower decoding error rate.
Estimating accurately channel noise has significant impact on the performance of channel coding. In this paper, we present a low complexity online estimator at the decoder side for low-density parity check (LDPC) codes over additive white Gaussian noise (AWGN) channels with a time-varying noise. The proposed algorithm is obtained by modeling the channel statistic as a Bayesian inference problem on a factor graph. Since BP algorithm cannot adapt efficiently to the statistical change of SNR in an AWGN channel, we apply the Laplace propagation (LP) algorithm on the proposed algorithm. Through simulations, we show that the proposed algorithm can simultaneously decode LDPC codes and estimate the time-varying SNR at the bit-level, which enhance the BP decoding performance. Moreover, the proposed LP estimator shows a very low computational complexity.
In this paper, we propose the tree-structured expectation propagation (TEP) algorithm for low-density parity-check (LDPC) decoding over the binary additive white Gaussian noise (BI-AWGN) channel. By approximating the posterior distribution by a tree-structure factorization, the TEP has been proven to improve belief propagation (BP) decoding over the binary erasure channel (BEC). We show for the AWGN channel how the TEP decoder is also able to capture additional information disregarded by the BP solution, which leads to a noticeable reduction of the error rate for finite-length codes. We show that for the range of codes of interest, the TEP gain is obtained with a slight increase in complexity over that of the BP algorithm. An efficient way of constructing the tree-like structure is also described.
In this paper, we propose the tree-structured expectation propagation (TEP) algorithm for low-density parity-check (LDPC) decoding over the additive white Gaussian noise (AWGN) channel. By imposing a tree-like approximation over the graphical model of the code, this algorithm introduces pairwise marginal constraints over pairs of variables, which provide joint information of the variables related. Thanks to this, the proposed TEP decoder improves the performance of the standard belief propagation (BP) solution. An efficient way of constructing the tree-like structure is also described. The simulation results illustrate the TEP decoder gain in the finite-length regime, compared to the standard BP solution. For code lengths shorter than n = 512, the gain in the waterfall region achieves up to 0.25 dB. We also notice a remarkable reduction of the error floor.
In this paper, we investigate the performance of the belief propagation (BP) algorithm for decoding low-density parity-check codes over the additive white Gaussian noise channel when there is an incorrect estimate of the channel signal-to-noise ratio (SNR) (referred to as "SNR mismatch") at the decoder. At the extremes for over- and underestimation of SNR, the performance of BP tends to that of min-sum algorithm and the channel bit-error rate, respectively. Our results for regular codes indicate that the sensitivity to mismatch increases by increasing the variable-node degree and by decreasing the check-node degree. The effect of variable-node degree, however, appears to be more profound, such that at a given rate, the codes with the smallest variable and check degrees are more robust against SNR mismatch. For irregular codes, by comparing the thresholds of a few ensembles, we demonstrate that the ensemble which performs better in the absence of mismatch can perform worse in the presence of it. To obtain our asymptotic results, we propose a computationally efficient method based on the Gaussian approximation of density evolution in the presence of SNR mismatch. We also show that the asymptotic results are consistent with simulation results for codes with finite block lengths