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

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.

I. Introduction

Channel coding and decoding technologies are widely used in various communication systems as effective methods to ensure reliable transmission of information. At present, low-density parity-check (LDPC) codes [1] are able to yield the performance close to the Shannon capacity under AWGN channels with the low complexity belief-propagation (BP) decoding algorithm [2]. However, in practical communication systems, the noise may exhibit correlations. Especially in some special scenarios, correlated noise is non-Gaussian and exhibits an impulsive character [3]. For example, the underwater acoustic noise in sonar applications [3] and the atmospheric noise in radar communications [4]. Many studies have proven that the symmetric α-stable (SαS) distribution which is a non-Gaussian distribution with lager tailing is a very successful model for describing the impulsive characteristic [5]. And the Sαs distribution has a strong theoretical guarantee of the generalized central limit theorem [6].