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Computer Engineering and Science

Effects of the SNR Mismatch on Decoding the LDPC Codes

Zhang Er-yang

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The decoding of the LDPC codes by the belief propagation(BP) algorithm for the additive white Gaussian noise(AWGN) channel requires an accurate estimation of the signal-to-noise ratio(SNR) for the computation of the a posteriori probabilities(APPs) of the received bits that serve as the decoder inputs.An erroneous estimation of SNR at the decoder is referred to as SNR mismatch.In this paper,we study the effects of the SNR mismatch on the bit error rate(BER) performance of the LDPC codes for the AWGN channel.The correct-factor function is achieved by approximating the check node update equation of the BP algorithm.It is concluded that the effect of SNR under-estimation on decoding is more sensitive than SNR over-estimation based on the correct-factor function.The simulation results also indicate the conclsion.

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The decoding of the LDPC codes by the belief propagation(BP) algorithm for the additive white Gaussian noise(AWGN) channel requires an accurate estimation of the signal-to-noise ratio(SNR) for the computation of the a posteriori probabilities(APPs) of the received bits that serve as the decoder inputs.An erroneous estimation of SNR at the decoder is referred to as SNR mismatch.In this paper,we study the effects of the SNR mismatch on the bit error rate(BER) performance of the LDPC codes for the AWGN channel.The correct-factor function is achieved by approximating the check node update equation of the BP algorithm.It is concluded that the effect of SNR under-estimation on decoding is more sensitive than SNR over-estimation based on the correct-factor function.The simulation results also indicate the conclsion.
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
Recently one decoding algorithm called as beyond belief propagation (BP) algorithm for LDPC Codes is derived using the knowledge of trapping set and different from standard BP algorithm, whose performance outperforms that of the latter over binary symmetric channel (BSC). However, the former is not suitable for additive white Gaussian noise (AWGN) channel. In this paper how to improve bit error rate (BER) performance of Beyond BP Algorithm is investigated over AWGN channel. It is found that this algorithm can be modified through setting appropriate penalty factor and obtains better performance than BP one over AWGN channel. The simulation results show dependently on choosing penalty factor modified Beyond BP Algorithm outperforms BP one over AWGN channel in high signal noise rate (SNR) region or almost whole SNR one and there are some differences for different code rates. Concretely, for medium or low code rate proposed algorithm can obtain more performance gain relative to high one when short frame is used.
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.
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.
Under the condition of the Additive White Gaussian Noise(AWGN) channel,both the hard and soft decision decoding algorithms suitable for LDPC codes are simulated and comparatively analyzed based on analyzing the decoding algorithm for LDPC codes.The variable message correlation for Log-Likelihood-Ratio Belief-Propagation(LLR-BP) algorithm in soft decision algorithm is decreased by introducing a multiplicative correction factor.The simulation results show that the decoding error-correction performance of the modified LLR-BP algorithm is greatly improved with little increase of computing complexity.
Designing realizable Maximum Likelihood (ML) decoders for low-density parity-check (LDPC) codes has always been a challenging problem. Maxwell decoder is a well-known ML decoder for LDPC codes over a binary erasure channel (BEC). Based on the concept used in the Maxwell decoder, it may be possible to design near-ML decoders for LDPC codes over an additive white Gaussian noise (AWGN) channel. In this paper, we introduce a novel idea called channel transformation, which will be used as a bridge linking a BEC channel and an AWGN channel. With the transformation, we further propose a near-ML decoder for LDPC codes sent over an AWGN channel. The proposed near-ML decoder, combining a Belief Propagation (BP) decoder and a Maxwell decoder, is called the BP-Maxwell (BM) decoder. Simulation results show that compared with a BP decoder, the BM decoding algorithm can accomplish better frame error rates (FERs) by eliminating many of the error frames with a smaller percentage of error bits. Thus, the BM decoder is a step closer to the ML decoder compared with the BP decoder.