Traditional Belief Propagation Research Articles

Polar-Coded Cooperation With Optimized Relay Selection in Multi-Satellite and Wireless Integrated Systems

Optimized polar-coded cooperation with an approximate prior probability-based threshold decision is proposed to improve the reliability and complexity in selective decode-and-forward (SDF) cooperation of multiple satellite constellation systems. First, an SDF scheme with polar coding is adopted in cooperative communications for efficient code construction and relay forwarding. Second, in the logarithmic belief propagation (BP) polar decoding, the variable iterative threshold is derived with independent and variable signal-to-noise ratio (SNR)-based approximate prior probability. This threshold reduces complexity by eliminating active nodes with high reliability in each decoding iteration. Third, the information detection factor is introduced to evaluate the accuracy of decoded bits, thereby limiting the average decoding iterations to improve decoding efficiency. Simulation results show that the proposed polar-coded SDF cooperation obtains 1.5 dB performance gain at a bit error rate (BER) of 10-3 compared with that of existing LDPC-related schemes. The complexity of the optimized logarithmic BP decoding is reduced by 25%–50% compared with that of the traditional BP decoding. Therefore, the proposed scheme has good BER performance and low complexity in cooperative communications of multi-satellite and wireless integrated systems.

An Asymmetric-Error-Aware LDPC Decoding Algorithm for DNA Storage

With the rapid growth of data, DNA is attracting attention as a promising storage medium due to its durability, large storage capacity, and high bulk density. However, errors occur in DNA synthesis and sequencing processes, with substitutions being the most common errors in DNA storage process. To address this issue, we select low-density parity-check (LDPC) codes as the error correction method to guarantee data reliability. However, unlike traditional data storage channels, errors occurring between nucleotides in the DNA channel are asymmetric. Therefore, traditional belief propagation (BP) decoding algorithm is not sufficient for effective error correction under DNA channel. In this letter, we propose to use two LDPC codes and take error types as additional information for calibrating log-likelihood ratio (LLR) value. In addition, compared with previous works, simulation results show that our proposed decoding algorithm can reduce bit error rate (BER) by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$33\% \sim 94\% $ </tex-math></inline-formula> .

Hierarchical Belief Propagation on Image Segmentation Pyramid.

The Markov random field (MRF) for stereo matching can be solved using belief propagation (BP). However, the solution space grows significantly with the introduction of high-resolution stereo images and 3D plane labels, making the traditional BP algorithms impractical in inference time and convergence.We present an accurate and efficient hierarchical BP framework using the representation of the image segmentation pyramid (ISP). The pixel-level MRF can be solved by a top-down inference on the ISP. We design a hierarchy of MRF networks using the graph of superpixels at each ISP level. From the highest/image to the lowest/pixel level, the MRF models can be efficiently inferred with constant global guidance using the optimal labels of the previous level. The large texture-less regions can be handled effectively by the MRF model on a high level. The advanced 3D continuous labels and a novel support-points regularization are integrated into our framework for stereo matching. We provide a data-level parallelism implementation which is orders of magnitude faster than the best graph cuts (GC) algorithm. The proposed framework, HBP-ISP, outperforms the best GC algorithm on the Middlebury stereo matching benchmark.

Channel Noise Optimization of Polar Codes Decoding Based on a Convolutional Neural Network

Polar code has the characteristics of simple coding and high reliability, and it has been used as the control channel coding scheme of 5G wireless communication. However, its decoding algorithm always encounters problems of large decoding delay and high iteration complexity when dealing with channel noise. To address the above challenges, this paper proposes a channel noise optimized decoding scheme based on a convolutional neural network (CNN). Firstly, a CNN is adopted to extract and train the colored channel noise to get more accurate estimation noise, and then, the belief propagation (BP) decoding algorithm is used to decode the polar codes based on the output of the CNN. To analyze and verify the performance of the proposed channel noise optimized decoding scheme, we simulate the decoding of polar codes with different correlation coefficients, different loss function parameters, and different code lengths. The experimental results show that the CNN-BP concatenated decoding can better suppress the colored channel noise and significantly improve the decoding gain compared with the traditional BP decoding algorithm.

Perturbed Adaptive Belief Propagation Decoding for High-Density Parity-Check Codes

Algebraic codes such as BCH code are receiving renewed interest as their short block lengths and low/no error floors make them attractive for ultra-reliable low-latency communications (URLLC) in 5G wireless networks. This article aims at enhancing the traditional adaptive belief propagation (ABP) decoding, which is a soft-in-soft-out (SISO) decoding for high-density parity-check (HDPC) algebraic codes, such as Reed-Solomon (RS) codes, Bose-Chaudhuri-Hocquenghem (BCH) codes, and product codes. The key idea of traditional ABP is to sparsify certain columns of the parity-check matrix corresponding to the least reliable bits with small log-likelihood-ratio (LLR) values. This sparsification strategy may not be optimal when some bits have large LLR magnitudes but wrong signs. Motivated by this observation, we propose a Perturbed ABP (P-ABP) to incorporate a small number of unstable bits with large LLRs into the sparsification operation of the parity-check matrix. In addition, we propose to apply partial layered scheduling or hybrid dynamic scheduling to further enhance the performance of P-ABP. Simulation results show that our proposed decoding algorithms lead to improved error correction performances and faster convergence rates than the prior-art ABP variants.

A Low Complexity Decoding Scheme for Raptor-Like LDPC Codes

Recently, a new structure of low density parity check (LDPC) code named raptor-like LDPC code has attracted much attention. It has better performance at low code rate. In this paper, a novel decoding scheme for raptor-like LDPC code is proposed. First, the Gaussian approximation density evolution (GADE) algorithm is used to track and analyze the message transmission during the decoding process. It is found that certain log likelihood ratio (LLR) messages can be approximated by “zero” setting in the early iteration of raptor-like LDPC decoding. In other words, some column and row operations could be eliminated without compromise the performance. Next, we propose a new decoding scheme, which can skip unnecessary column and row operations. In comparison with the traditional belief propagation (BP)-based LDPC decoding scheme, the proposed scheme can reduce the decoding complexity. Additionally, a new algorithm is developed to facilitate the selection of the early iteration number. With this novel design, the proposed decoding scheme performs almost the same as the traditional BP-based scheme. To proof the concept, the raptor-like LDPC codes in the ATSC3.0 digital TV system are used to evaluate the proposed scheme, in comparison with the traditional BP-based schemes, i.e., sum-product algorithm (SPA), offset min-sum algorithm (OMSA), and normalized min-sum algorithm (NMSA). The simulation results confirm that the proposed scheme can reduce the decoding complexity without sacrifice in performance for all SPA, OMSA, and NMSA methods. About 10% complexity reduction can be achieved. This will reduce the buttery consumption for Internet of Things (IoT) and handheld devices.

Joint Shuffled Scheduling Decoding Algorithm for DP-LDPC Codes-Based JSCC Systems

In this letter, a joint shuffled scheduling decoding algorithm for double-protograph low-density parity-check (DP-LDPC) codes-based joint source-channel coding (JSCC) schemes is presented. The proposed algorithm adopts the shuffled scheduling method to both source decoder and channel decoder, and can improve convergence speed and reduce the decoding complexity. In addition, a unique phenomenon named unequal convergence rates is revealed at the same time. The proposed algorithm can terminate this phenomenon with faster decoding. The results show that this algorithm has faster convergence speed and better error performance, compared with the traditional joint belief propagation (BP) decoding algorithm.

A Low-Complexity Belief Propagation Based Decoding Scheme for Polar Codes - Decodability Detection and Early Stopping Prediction

In the 5G communication systems, polar code has been adapted as the control channel coding solution in the enhanced mobile broadband (eMBB) scenario. Although different decoding schemes, including belief propagation (BP) and successive cancellation (SC) based algorithms, have been proposed, the decoding complexity as well as the latency are still significant. To address this critical issue, several low-complexity schemes, e.g., the use of simplified decoding operation and stop the decoding operation in earlier stage, have been proposed recently. However, conventional early stopping strategies have to check a pre-defined metric in each iteration, and the associated decoding delay is significant. In this paper, to address this challenge, we proposed a low-complexity BP based decoding scheme, which contains the decodability detection stage and the early stopping prediction stage. The decodability detection stage can identify the codewords in the deep channel fading environment and eliminate the unnecessary decoding operations to reduce the decoding complexity, while the early stopping prediction stage can directly predict the required number of iterations rather than checking the metric in each iteration to avoid the associated decoding delay. Through the above two approaches, our proposed scheme is shown to achieve 71% decoding delay reduction and maintain the same decoding performance as traditional BP, G-matrix, MinLLR schemes.

Extended Belief Propagation Decoding of Luby Transform Codes for the Small Number of Encoded Packets

Rateless coding such as Luby transform (LT) codes is representative of rate adaptive solutions to improve the frequency efficiency of transmitting data over a time-varying wireless channel. Also, these type of codes use belief propagation (BP) decoding which searches for encoded packets with degree 1 among the large numbers of encoded packets. This method fails if no encoded packets with degree 1 exist. However, in reality, small numbers of input packets are often encountered. In this paper, we have proposed a decoding algorithm that increases the performance of these codes for the small number of source packets. After the failure of BP decoding, to recover the remaining source packets, we use a method which keeps on decoding using the encoded packets whose degrees are not one. This algorithm continues until a degree 1 packet emerges in one of the iterations of this decoding process. Then, decoding algorithm switches back to the traditional BP decoding.

Detection-Free Multiobject Tracking by Reconfigurable Inference With Bundle Representations.

This paper presents a conceptually simple but effective approach to track multiobject in videos without requiring elaborate supervision (i.e., training object detectors or templates offline). Our framework performs a bi-layer inference of spatio-temporal grouping to exploit rich appearance and motion information in the observed sequence. First, we generate a robust middle-level video representation based on clustered point tracks, namely video bundles. Each bundle encapsulates a chunk of point tracks satisfying both spatial proximity and temporal coherency. Taking the video bundles as vertices, we build a spatio-temporal graph that incorporates both competitive and compatible relations among vertices. The multiobject tracking can be then phrased as a graph partition problem under the Bayesian framework, and we solve it by developing a reconfigurable belief propagation (BP) algorithm. This algorithm improves the traditional BP method by allowing a converged solution to be reconfigured during optimization, so that the inference can be reactivated once it gets stuck in local minima and thus conduct more reliable results. In the experiments, we demonstrate the superior performances of our approach on the challenging benchmarks compared with other state-of-the-art methods.

Accurate and Fast Convergent Initial-Value Belief Propagation for Stereo Matching.

The belief propagation (BP) algorithm has some limitations, including ambiguous edges and textureless regions, and slow convergence speed. To address these problems, we present a novel algorithm that intrinsically improves both the accuracy and the convergence speed of BP. First, traditional BP generally consumes time due to numerous iterations. To reduce the number of iterations, inspired by the crucial importance of the initial value in nonlinear problems, a novel initial-value belief propagation (IVBP) algorithm is presented, which can greatly improve both convergence speed and accuracy. Second, .the majority of the existing research on BP concentrates on the smoothness term or other energy terms, neglecting the significance of the data term. In this study, a self-adapting dissimilarity data term (SDDT) is presented to improve the accuracy of the data term, which incorporates an additional gradient-based measure into the traditional data term, with the weight determined by the robust measure-based control function. Finally, this study explores the effective combination of local methods and global methods. The experimental results have demonstrated that our method performs well compared with the state-of-the-art BP and simultaneously holds better edge-preserving smoothing effects with fast convergence speed in the Middlebury and new 2014 Middlebury datasets.

Accurate Belief Propagation with parametric and non-parametric measure for stereo matching

Stereo matching is one of the most active research areas in computer vision. Recently, Belief Propagation algorithm based on global optimization has great advances. However, traditional data term of Belief Propagation algorithm mainly lies on pixels-based intensity measure, and its effect is not very well. In this paper, a novel stereo matching is proposed that utilizes Census measure and pixels-based intensity measure into data term of Belief Propagation algorithm. But only simply adding Census measure is not enough to improve the accuracy of Belief Propagation, therefore the post procession for the algorithm is very essential. We combine intensity measure with Census algorithm into data term of Belief Propagation algorithm and acquire more accurate results by using the post procession. This proposed method may be more exacter than traditional Belief Propagation algorithm. The experimental results demonstrate the superior performance of our proposed method.

A novel decoding algorithm based on the hierarchical reliable strategy for SCG-LDPC codes in optical communications

An effective hierarchical reliable belief propagation (HRBP) decoding algorithm is proposed according to the structural characteristics of systematically constructed Gallager low-density parity-check (SCG-LDPC) codes. The novel decoding algorithm combines the layered iteration with the reliability judgment, and can greatly reduce the number of the variable nodes involved in the subsequent iteration process and accelerate the convergence rate. The result of simulation for SCG-LDPC(3969,3720) code shows that the novel HRBP decoding algorithm can greatly reduce the computing amount at the condition of ensuring the performance compared with the traditional belief propagation (BP) algorithm. The bit error rate (BER) of the HRBP algorithm is considerable at the threshold value of 15, but in the subsequent iteration process, the number of the variable nodes for the HRBP algorithm can be reduced by about 70% at the high signal-to-noise ratio (SNR) compared with the BP algorithm. When the threshold value is further increased, the HRBP algorithm will gradually degenerate into the layered-BP algorithm, but at the BER of 10−7 and the maximal iteration number of 30, the net coding gain (NCG) of the HRBP algorithm is 0.2 dB more than that of the BP algorithm, and the average iteration times can be reduced by about 40% at the high SNR. Therefore, the novel HRBP decoding algorithm is more suitable for optical communication systems.

Dense Corresponding Pixel Matching Between Aerial Epipolar Images Using an RGB-Belief Propagation Algorithm

A new algorithm, RGB-belief propagation (RGBBP), for dense corresponding pixel matching between aerial epipolar images is proposed in this letter. Evolved from the traditional belief-propagation algorithm, RGB-BP makes full use of all the three color components, R, G, and B, and simplifies the parameter settings. In order to reduce the impact of the obvious color differences between corresponding pixels, RGB-BP reduces the sensitivity of central pixels and increases the contribution of neighboring pixels. Three pairs of aerial epipolar images are tested using RGB-BP. The experimental results demonstrate the effectiveness of RGB-BP.

Noise Adaptive LDPC Decoding Using Particle Filtering

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.

Finite alphabet iterative decoders for LDPC codes surpassing floating-point iterative decoders

Introduced is a new type of message-passing (MP) decoders for low-density parity-check (LDPC) codes over the binary symmetric channel. Unlike traditional belief propagation (BP) based MP algorithms which propagate probabilities or log-likelihoods, the new MP decoders propagate messages requiring only a finite number of bits for their representation in such a way that good performance in the error floor region is ensured. Additionally, these messages are not quantised probabilities or log-likelihoods. As examples, MP decoders are provided that require only three bits for message representation, but surpass the floating-point BP (which requires a large number of bits for representation) in the error-floor region.

An Improved Belief-Propagation Decoder for LDPC-Coded Partial-Response Channels

The traditional belief-propagation (BP) decoder for low-density parity-check (LDPC) codes assumes that the soft input information for each bit is independent of all other bits. However, for partial-response (PR) channels, the log-likelihood ratios (LLRs) generated by the channel detector are correlated. In this paper, we propose an improved BP (IBP) decoder to take into account the dependence among the LLRs produced by channel detectors. The IBP decoder needs not only the LLR for each bit but also the probability distribution of the subblock that contains this bit. Therefore, we revise the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm accordingly to generate the additional information during channel detection. We apply the proposed decoder to an ideal PR channel and, as a practical example, to equalized perpendicular magnetic recording channels (PMRCs). The IBP decoder significantly outperforms the traditional BP decoder without turbo equalization, but this gain is substantially reduced when we introduce turbo equalization. Furthermore, we extend the IBP decoder to nonbinary LDPC codes, and show that we can achieve additional gains.

Research of an improved BP decoding arithmetic

PurposeThe purpose of this paper is to research the traditional belief‐propagation (BP) decoding algorithm of low‐density parity‐check code. The big computation load is a shortcoming of traditional BP decoding algorithm. Accordingly, the paper provides an improved BP decoding algorithm which raises the decoding efficiency and reduces decoding time delay.Design/methodology/approachAn improved BP decoding algorithm is studied and the error correction performance of the improved BP decoding algorithm in the Gaussian channel is provided.FindingsThe simulation result shows the improved BP decoding algorithm has lower computational complexity and higher decoding speed based on the premise of a little decoding performance loss.Research limitations/implicationsThe improved BP decoding algorithm has lower computational complexity and higher decoding speed based on the premise of a little decoding performance loss.Practical implicationsThe improved BP decoding algorithm raises the decoding efficiency and reduces decoding time delay.Originality/valueThe decoding algorithm only needs to update the wrong bit information which might arise, but not update the bit information whose reliability is very high. The improved BP decoding algorithm raises the decoding efficiency and reduces decoding time delay.

Loopy Belief Propagation: Convergence and Effects of Message Errors

Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether due to quantization of the messages or model parameters, from other simplified message or model representations, or from stochastic approximation methods. The introduction of such errors into the BP message computations has the potential to affect the solution obtained adversely. We analyze the effect resulting from message approximation under two particular measures of error, and show bounds on the accumulation of errors in the system. This analysis leads to convergence conditions for traditional BP message passing, and both strict bounds and estimates of the resulting error in systems of approximate BP message passing.