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IEEE International Conference on Signal, Information and Data Processing (ICSIDP)

Modified Iterative BP-CNN Decoder Under Correlated Noise with Symmetric α-stable Distributions

Senlin Li, Sihui Zheng, Jingwen Zhang, Xiang Chen, Zesong Fei

Published Dec 1, 2019• 0 citations
Publisher

Abstract

Recently, an iterative belief propagation-convolutional neural network (BP-CNN) decoder has been proposed to process the low-density parity-check (LDPC) decoding under correlated noise. However, in many practical scenarios, correlated noise may have extra special characteristics, such as impulse. Therefore, when used in such scenarios, there will be some space for the performance improvement of the BP-CNN decoder, since its loss functions cannot make full use of the special characteristics of correlated noise. Fortunately, the impulsive property of correlated noise can be effectively described by the symmetric α-stable (SαS) distribution model. Thus, we propose a novel loss function to train a well-behaved CNN model under correlated noise with SαS distributions. In order to take advantage of the features of SαS distributions captured by CNN, the proposed loss function involves a probability density function (PDF) estimation of the residual noise and a similarity detection. The similarity detection uses the Kullback-Leibler (KL) divergence method to compare the similarity between the estimated PDF and the Gaussian distribution. In the BP-CNN decoder, the residual noise is defined as the difference between the actual noise and the estimated noise. The effectiveness of our modifications for the BP-CNN decoder will be demonstrated with simulation results.

DOI
10.1109/icsidp47821.2019.9172958

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Recently, an iterative belief propagation-convolutional neural network (BP-CNN) decoder has been proposed to process the low-density parity-check (LDPC) decoding under correlated noise. However, in many practical scenarios, correlated noise may have extra special characteristics, such as impulse. Therefore, when used in such scenarios, there will be some space for the performance improvement of the BP-CNN decoder, since its loss functions cannot make full use of the special characteristics of correlated noise. Fortunately, the impulsive property of correlated noise can be effectively described by the symmetric α-stable (SαS) distribution model. Thus, we propose a novel loss function to train a well-behaved CNN model under correlated noise with SαS distributions. In order to take advantage of the features of SαS distributions captured by CNN, the proposed loss function involves a probability density function (PDF) estimation of the residual noise and a similarity detection. The similarity detection uses the Kullback-Leibler (KL) divergence method to compare the similarity between the estimated PDF and the Gaussian distribution. In the BP-CNN decoder, the residual noise is defined as the difference between the actual noise and the estimated noise. The effectiveness of our modifications for the BP-CNN decoder will be demonstrated with simulation results.
Abstract Low-density parity-check (LDPC) codes, particularly nonbinary LDPC (NB-LDPC) codes, are essential for meeting the high peak data rate requirements of the 6th generation systems. However, challenges arise from correlated noise, caused by factors like seasonal variations and inaccuracies in signal-to-noise ratio estimation, which hinder their practical deployment. In this paper, we propose a convolutional neural network-aided iterative detection and decoding (CNN-IDD) method for NB-LDPC coded modulation systems, aiming to enhance performance over correlated noise channels with a slight increase in complexity. In this system, a convolutional neural network (CNN) is integrated with iterative hard-reliability-based algorithms to learn from the correlated noise. The CNN and the hard-decision decoder interact iteratively to mitigate noise effects and improve estimation accuracy. Simulation results show that the proposed scheme achieves up to 1 dB improvement in performance, while maintaining the low complexity advantage of traditional hard-reliability decoding for high-order modulation in NB-LDPC systems over correlated noise channels.
Today's modern wireless communication systems demand extensive quality and computational power with an increase in day-to-day data-rate standards. The latest com-munication standards focus on low latency, high throughput, and reliable error correction capabilities which inspired us to explore the 5G New Generation (NR) technology. Low-Density Parity-Check Codes (LDPC) are known to have error correction capabilities that can achieve Shannon's maximum channel ca-pacity. Encoding of LDPC Codes features a sparse property that enables effortless decoding at the receiver end. Advancements in deep learning have helped in estimating the channel noise more accurately. The Iterative Belief Propagation-Convolutional Neural Network (BP-CNN) architecture involves a CNN block which is trained with a quadratic loss function concatenated to a standard BP Decoder. The proposed Iterative BP-CNN architecture with a Batch Normalization layer results in a better performance compared to the Iterative BP-CNN architecture as it standardizes the input to the CNN block and also solves the problem of vanishing gradients during backpropagation.
To combat the correlated noise and utilize the non-equiprobability of the source, we propose a novel Low-density parity-check (LDPC) decoder design based on a priori information and neural network, which includes two neural networks, namely Correlated-Denoising Convolutional Neural Network (Correlated-DnCNN) and Belief Propagation-Deep Neural Network (BP-DNN), respectively. Correlated-DnCNN is used to remove the correlation of channel noise and reduce the noise power. BP-DNN is used to eliminate the harmful effect of short cycles of the Tanner graph and explore the priori information of the source. With the priori information to assist in initializing the input nodes of the BP-DNN network, we introduce compression capability to the LDPC, thus the proposed scheme can improve efficiency significantly when there is a large amount of compressible data in the physical layer. To train the Correlated-DnCNN and BP-DNN jointly, we design a new three-objective joint denoising-decoding loss function, which can not only guarantee the decoding performance, but also constrain the noise to conform to the normal distribution as much as possible, and improve the network convergence performance. Experiments show that the proposed decoding framework can remove the noise correlation, reduce the noise power, and improve the decoding performance effectively.
In long wave communication scenarios, channel interferences lead to noise correlation. Since traditional belief propagation (BP) decoding algorithm is designed based on additive white Gaussian noise (AWGN), a performance cost will appear when it comes to correlated noise. In this paper, a new LDPC decoding scheme that applies to correlated Gaussian noise is proposed. We design a BP-gated neural network-BP structure to carry on two rounds of BP decoding with the second round based on optimized noise. By adopting gated neurons in typical NN, CNN, training performance is improved. Simulation shows that compared with BP decoding algorithm, the new decoding scheme outperforms traditional method by 0.5~0.61 dB when bit error rate is 10-6. This decoding scheme also works on pectinate noise with performance gain of 1.5 dB.
The performance of Low-Density Parity-Check codes over symmetric alpha-stable impulsive noise channels is considered in this paper. Due to the lack of closed-form expressions for the probability density functions of almost all the alpha-stable distributions, an efficient non-linear approximation method for channel log-likelihood ratio is presented to achieve high decoding performance covering the range of characteristic exponent from 1 to 2 and avoid the use of complicated numerical integrations. The simulations for both long and short codes show that the parameter selection of the proposed method is not sensitive to the noise level. Even fixed parameter setting for the proposed non-linear approximation can obtain a satisfying decoding performance.