Improved Belief Propagation Decoder for LDPC-CRC-Polar Codes with Bit-Freezing

Though belief propagation bit-flip(BPBF)decoding improves the error correction performance of polar codes,it uses the exhaustive flips method to achieve the error correction performance of CA-SCL decoding,thus resulting in high decoding complexity and latency.To alleviate this issue,we incorporate the LDPC-CRC-Polar coding scheme with BPBF and propose an improved belief propagation decoder for LDPC-CRC-Polar codes with bit-freezing(LDPCCRC-Polar codes BPBFz).The proposed LDPCCRC-Polar codes BPBFz employs the LDPC code to ensure the reliability of the flipping set,i.e.,critical set(CS),and dynamically update it.The modified CS is further utilized for the identification of error-prone bits.The proposed LDPC-CRC-Polar codes BPBFz obtains remarkable error correction performance and is comparable to that of the CA-SCL(L=16)decoder under medium-to-high signal-to-noise ratio(SNR)regions.It gains up to 1.2dB and 0.9dB at a fixed BLER=10-4compared with BP and BPBF(CS-1),respectively.In addition,the proposed LDPC-CRC-Polar codes BPBFz has lower decoding latency compared with CA-SCL and BPBF,i.e.,it is 15 times faster than CA-SCL(L=16)at high SNR regions.

Improved Segmented Belief Propagation List Decoding for Polar Codes with Bit-Flipping

Belief propagation list(BPL) decoding for polar codes has attracted more attention due to its inherent parallel nature. However, a large gap still exists with CRC-aided SCL(CA-SCL) decoding.In this work, an improved segmented belief propagation list decoding based on bit flipping(SBPL-BF) is proposed. On the one hand, the proposed algorithm makes use of the cooperative characteristic in BPL decoding such that the codeword is decoded in different BP decoders. Based on this characteristic, the unreliable bits for flipping could be split into multiple subblocks and could be flipped in different decoders simultaneously. On the other hand, a more flexible and effective processing strategy for the priori information of the unfrozen bits that do not need to be flipped is designed to improve the decoding convergence. In addition, this is the first proposal in BPL decoding which jointly optimizes the bit flipping of the information bits and the code bits. In particular, for bit flipping of the code bits, a H-matrix aided bit-flipping algorithm is designed to enhance the accuracy in identifying erroneous code bits. The simulation results show that the proposed algorithm significantly improves the errorcorrection performance of BPL decoding for medium and long codes. It is more than 0.25 d B better than the state-of-the-art BPL decoding at a block error rate(BLER) of 10^(-5), and outperforms CA-SCL decoding in the low signal-to-noise(SNR) region for(1024, 0.5)polar codes.

分组衰落信道下LDPC的一种带信道估计的改进Belief-Propagation算法

该文首先通过仿真证明了LDPC(Low Density Parity Check code)在分组衰落信道下,以通常的 Belief-propagation算法译码,具有较好性能。然后基于算法的特殊迭代特性,提出分组衰落信道下,在每一迭代步 骤中结合信道估计的改进的Belief-propagation算法。仿真证明,该算法可以有效地减少译码迭代次数。

VARIABLE NON-UNIFORM QUANTIZED BELIEF PROPAGATION ALGORITHM FOR LDPC DECODING

Non-uniform quantization for messages in Low-Density Parity-Check(LDPC)decoding canreduce implementation complexity and mitigate performance loss.But the distribution of messagesvaries in the iterative decoding.This letter proposes a variable non-uniform quantized Belief Propaga-tion(BP)algorithm.The BP decoding is analyzed by density evolution with Gaussian approximation.Since the probability density of messages can be well approximated by Gaussian distribution,by theunbiased estimation of variance,the distribution of messages can be tracked during the iteration.Thusthe non-uniform quantization scheme can be optimized to minimize the distortion.Simulation resultsshow that the variable non-uniform quantization scheme can achieve better error rate performance andfaster decoding convergence than the conventional non-uniform quantization and uniform quantizationschemes.

Distributed Resource Allocation in Ultra-Dense Networks via Belief Propagation

Ultra-dense networking is widely accepted as a promising enabling technology to realize high power and spectrum efficient communications in future 5G communication systems. Although joint resource allocation schemes promise huge performance improvement at the cost of cooperation among base stations,the large numbers of user equipment and base station make jointly optimizing the available resource very challenging and even prohibitive. How to decompose the resource allocation problem is a critical issue. In this paper,we exploit factor graphs to design a distributed resource allocation algorithm for ultra dense networks,which consists of power allocation,subcarrier allocation and cell association. The proposed factor graph based distributed algorithm can decompose the joint optimization problem of resource allocation into a series of low complexity subproblems with much lower dimensionality,and the original optimization problem can be efficiently solved via solving these subproblems iteratively. In addition,based on the proposed algorithm the amounts of exchanging information overhead between the resulting subprob-lems are also reduced. The proposed distributed algorithm can be understood as solving largely dimensional optimization problem in a soft manner,which is much preferred in practical scenarios. Finally,the performance of the proposed low complexity distributed algorithm is evaluated by several numerical results.

A Memory Efficient Belief Propagation Decoder for Polar Codes

Polar codes have become increasingly popular recently because of their capacity achieving property.In this paper,a memory efficient stage-combined belief propagation(BP) decoder design for polar codes is presented.Firstly,we briefly reviewed the conventional BP decoding algorithm.Then a stage-combined BP decoding algorithm which combines two adjacent stages into one stage and the corresponding belief message updating rules are introduced.Based on this stage-combined decoding algorithm,a memory-efficient polar BP decoder is designed.The demonstrated decoder design achieves 50%memory and decoding latency reduction in the cost of some combinational logic complexity overhead.The proposed decoder is synthesized under TSMC 45 nm Low Power CMOS technology.It achieves 0.96 Gb/s throughput with 14.2mm^2 area when code length N=2^(16)which reduces 51.5%decoder area compared with the conventional decoder design.

Convergence Rate Analysis of Gaussian Belief Propagation for Markov Networks

Gaussian belief propagation algorithm(GaBP) is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density functions from a high dimensional joint density function over a Markov network in a finite number of iterations when the underlying Gaussian graph is acyclic. It is also known more recently that the algorithm produces correct marginal means asymptotically for cyclic Gaussian graphs under the condition of walk summability(or generalised diagonal dominance). This paper extends this convergence result further by showing that the convergence is exponential under the generalised diagonal dominance condition,and provides a simple bound for the convergence rate. Our results are derived by combining the known walk summability approach for asymptotic convergence analysis with the control systems approach for stability analysis.

Link prediction in complex networks via modularity-based belief propagation

Link prediction aims at detecting missing, spurious or evolving links in a network, based on the topological information and/or nodes＇ attributes of the network. Under the assumption that the likelihood of the existence of a link between two nodes can be captured by nodes＇ similarity, several methods have been proposed to compute similarity directly or indirectly, with information on node degree. However, correctly predicting links is also crucial in revealing the link formation mechanisms and thus in providing more accurate modeling for networks. We here propose a novel method to predict links by incorporating stochastic-block-model link generating mechanisms with node degree. The proposed method first recov- ers the underlying block structure of a network by modularity-based belief propagation, and based on the recovered block structural information it models the link likelihood between two nodes to match the degree sequence of the network. Experiments on a set of real-world networks and synthetic networks generated by stochastic block model show that our proposed method is effective in detecting missing, spurious or evolving links of networks that can be well modeled by a stochastic block model. This approach efficiently complements the toolbox for complex network analysis, offering a novel tool to model links in stochastic block model networks that are fundamental in the modeling of real world complex networks.

Iterative Receiver for Orthogonal Time Frequency Space with Index Modulation via Structured Prior-Based Hybrid Belief and Expectation Propagation

Orthogonal Time Frequency Space(OTFS)signaling with index modulation(IM)is a promising transmission scheme characterized by high transmission efficiency for high mobility scenarios.In this paper,we study the receiver for coded OTFS-IM system.First,we construct the corresponding factor graph,on which the structured prior incorporating activation pattern constraint and channel coding is devised.Then we develop a iterative receiver via structured prior-based hybrid belief propagation(BP)and expectation propagation(EP)algorithm,named as StrBP-EP,for the coded OTFS-IM system.To reduce the computational complexity of discrete distribution introduced by structured prior,Gaussian approximation conducted by EP is adopted.To further reduce the complexity,we derive two variations of the proposed algorithm by using some approximations.Simulation results validate the superior performance of the proposed algorithm.

Low-loss belief propagation decoder with Tanner graph in quantum error-correction codes

Quantum error-correction codes are immeasurable resources for quantum computing and quantum communication.However,the existing decoders are generally incapable of checking node duplication of belief propagation(BP)on quantum low-density parity check(QLDPC)codes.Based on the probability theory in the machine learning,mathematical statistics and topological structure,a GF(4)(the Galois field is abbreviated as GF)augmented model BP decoder with Tanner graph is designed.The problem of repeated check nodes can be solved by this decoder.In simulation,when the random perturbation strength p=0.0115-0.0116 and number of attempts N=60-70,the highest decoding efficiency of the augmented model BP decoder is obtained,and the low-loss frame error rate(FER)decreases to 7.1975×10^(-5).Hence,we design a novel augmented model decoder to compare the relationship between GF(2)and GF(4)for quantum code[[450,200]]on the depolarization channel.It can be verified that the proposed decoder provides the widely application range,and the decoding performance is better in QLDPC codes.

Belief Propagation List Decoding for Polar Codes:Performance Analysis and Software Implementation on GPU

Belief propagation(BP)decoding outputs soft information and can be naturally used in iterative receivers.BP list(BPL)decoding provides comparable error-correction performance to the successive cancellation list(SCL)decoding.In this paper,we firstly introduce an enhanced code construction scheme for BPL decoding to improve its errorcorrection capability.Then,a GPU-based BPL decoder with adoption of the new code construction is presented.Finally,the proposed BPL decoder is tested on NVIDIA RTX3070 and GTX1060.Experimental results show that the presented BPL decoder with early termination criterion achieves above 1 Gbps throughput on RTX3070 for the code(1024,512)with 32 lists under good channel conditions.

Parity-check and G-matrix based intelligent early stopping criterion for belief propagation decoder for polar codes

The error correction performance of Belief Propagation(BP)decoding for polar codes is satisfactory compared with the Successive Cancellation(SC)decoding.Nevertheless,it has to complete a fixed number of iterations,which results in high computational complexity.This necessitates an intelligent identification of successful BP decoding for early termination of the decoding process to avoid unnecessary iterations and minimize the computational complexity of BP decoding.This paper proposes a hybrid technique that combines the“paritycheck”with the“G-matrix”to reduce the computational complexity of BP decoder for polar codes.The proposed hybrid technique takes advantage of the parity-check to intelligently identify the valid codeword at an early stage and terminate the BP decoding process,which minimizes the overhead of the G-matrix and reduces the computational complexity of BP decoding.We explore a detailed mechanism incorporating the parity bits as outer code and prove that the proposed hybrid technique minimizes the computational complexity while preserving the BP error correction performance.Moreover,mathematical formulation for the proposed hybrid technique that minimizes the computation cost of the G-matrix is elaborated.The performance of the proposed hybrid technique is validated by comparing it with the state-of-the-art early stopping criteria for BP decoding.Simulation results show that the proposed hybrid technique reduces the iterations by about 90%of BP decoding in a high Signal-to-Noise Ratio(SNR)(i.e.,3.5~4 dB),and approaches the error correction performance of G-matrix and conventional BP decoder for polar codes.

A Survey on Belief Propagation Decoding of Polar Codes

The increasing data traffic rate of wireless communication systems forces the development of new technologies mandatory.Providing high data rate,extremely low latency and improvement on quality of service are the main subjects of next generation 5G wireless communication systems which will be in the people’s life in the years of 2020.As the newest and first mathematically proven forward error correction code,polar code is one of the best candidates among error correction methods that can be employed for 5G wireless networks.The aim of this tutorial is to show that belief propagation decoding of polar codes can be a promising forward error correction technique in upcoming 5G frameworks.First,we survey the novel approaches to the belief propagation based decoding of polar codes and continue with the studies about the simplification of these decoders.Moreover,early detection and termination methods and concept of scheduling are going to be presented throughout the manuscript.Finally,polar construction algorithms,error types in belief propagation based decoders and hardware implementations are going to be mentioned.Overall,this tutorial proves that the BP based decoding of polar codes has a great potential to be a part of communication standards.

A Multi-Vehicle Cooperative Localization Method Based on Belief Propagation in Satellite Denied Environment

The global navigation satellite system(GNSS)is currently being used extensively in the navigation system of vehicles.However,the GNSS signal will be faded or blocked in complex road environments,which will lead to a decrease in positioning accuracy.Owing to the higher-precision synchronization provided in the sixth generation(6G)network,the errors of ranging-based positioning technologies can be effectively reduced.At the same time,the use of terahertz in 6G allows excellent resolution of range and angle,which offers unique opportunities for multi-vehicle cooperative localization in a GNSS denied environment.This paper introduces a multi-vehicle cooperative localization method.In the proposed method,the location estimations of vehicles are derived by utilizing inertial measurement and then corrected by exchanging the beliefs with adjacent vehicles and roadside units.The multi-vehicle cooperative localization problem is represented using a factor graph.An iterative algorithm based on belief propagation is applied to perform the inference over the factor graph.The results demonstrate that our proposed method can offer a considerable capability enhancement on localization accuracy.

FORCE RIPPLE SUPPRESSION TECHNOLOGY FOR LINEAR MOTORS BASED ON BACK PROPAGATION NEURAL NETWORK

Various force disturbances influence the thrust force of linear motors when a linear motor （LM） is running. Among all of force disturbances, the force ripple is the dominant while a linear motor runs in low speed. In order to suppress the force ripple, back propagation（BP） neural network is proposed to learn the function of the force ripple of linear motors, and the acquisition method of training samples is proposed based on a disturbance observer. An off-line BP neural network is used mainly because of its high running efficiency and the real-time requirement of the servo control system of a linear motor. By using the function, the force ripple is on-line compensated according to the position of the LM. The experimental results show that the force ripple is effectively suppressed by the compensation of the BP neural network.

Simulation of phytoplankton biomass in Quanzhou Bay using a back propagation network model and sensitivity analysis for environmental variables

Prediction and sensitivity models,to elucidate the response of phytoplankton biomass to environmental factors in Quanzhou Bay,Fujian,China,were developed using a back propagation(BP) network.The environmental indicators of coastal phytoplankton biomass were determined and monitoring data for the bay from 2008 was used to train,test and build a three-layer BP artificial neural network with multi-input and single-output.Ten water quality parameters were used to forecast phytoplankton biomass(measured as chlorophyll-a concentration).Correlation coefficient between biomass values predicted by the model and those observed was 0.964,whilst the average relative error of the network was-3.46% and average absolute error was 10.53%.The model thus has high level of accuracy and is suitable for analysis of the influence of aquatic environmental factors on phytoplankton biomass.A global sensitivity analysis was performed to determine the influence of different environmental indicators on phytoplankton biomass.Indicators were classified according to the sensitivity of response and its risk degree.The results indicate that the parameters most relevant to phytoplankton biomass are estuary-related and include pH,sea surface temperature,sea surface salinity,chemical oxygen demand and ammonium.

基于GRU-BP算法的高精度动态物流称重系统

针对动态物流秤测量精度对载重、采样频率、带速较为敏感的问题,提出了一种高精度动态物流称重系统。首先,采用三因素五水平正交试验法,结合皮尔逊相关性检验原则,使用低通巴特沃斯与卡尔曼滤波器对传感器压力信号进行了滤波降噪处理,并将加速度信号作为模型输入信号,进行了特征补偿;然后,基于深度学习算法,提出了一种改进的门控循环单元模型,在该模型采样区间内将压力与振动改写为时序化信号,并将其共同输入门控循环单元(GRU)模型;最后,对GRU模型进行了改进,对其结构输出了层堆叠误差反向传播神经网络(BP),有效加强了模型的非线性映射能力。研究结果表明:在各类传动速度及测试货物下,该模型的最大测量误差相对于同类型深度学习模型长短期记忆(LSTM)神经网络、循环神经网络(RNN)时序模型及传统数值平均模型的误差,依次降低了16.14%、27.14%、76%,可用于各类称重系统。

Surface Quality Evaluation of Fluff Fabric Based on Particle Swarm Optimization Back Propagation Neural Network

Aiming at the problem that back propagation(BP)neural network predicts the low accuracy rate of fluff fabric after fluffing process,a BP neural network model optimized by particle swarm optimization(PSO)algorithm is proposed.The sliced image is obtained by the principle of light-cutting imaging.The fluffy region of the adaptive image segmentation is extracted by the Freeman chain code principle.The upper edge coordinate information of the fabric is subjected to one-dimensional discrete wavelet decomposition to obtain high frequency information and low frequency information.After comparison and analysis,the BP neural network was trained by high frequency information,and the PSO algorithm was used to optimize the BP neural network.The optimized BP neural network has better weights and thresholds.The experimental results show that the accuracy of the optimized BP neural network after applying high-frequency information training is 97.96%,which is 3.79%higher than that of the unoptimized BP neural network,and has higher detection accuracy.

Combinatorial Optimization Based Analog Circuit Fault Diagnosis with Back Propagation Neural Network

Electronic components' reliability has become the key of the complex system mission execution. Analog circuit is an important part of electronic components. Its fault diagnosis is far more challenging than that of digital circuit. Simulations and applications have shown that the methods based on BP neural network are effective in analog circuit fault diagnosis. Aiming at the tolerance of analog circuit,a combinatorial optimization diagnosis scheme was proposed with back propagation( BP) neural network( BPNN).The main contributions of this scheme included two parts:( 1) the random tolerance samples were added into the nominal training samples to establish new training samples,which were used to train the BP neural network based diagnosis model;( 2) the initial weights of the BP neural network were optimized by genetic algorithm( GA) to avoid local minima,and the BP neural network was tuned with Levenberg-Marquardt algorithm( LMA) in the local solution space to look for the optimum solution or approximate optimal solutions. The experimental results show preliminarily that the scheme substantially improves the whole learning process approximation and generalization ability,and effectively promotes analog circuit fault diagnosis performance based on BPNN.

Using Back Propagation Neural Network Method to Forecast Daily Indices of Solar Activity F_(10.7)

The solar 10.7 cm radio flux,F_(10.7),a measure of the solar radio flux per unit frequency at a wavelength of 10.7 cm,is a key and serviceable index for monitoring solar activities.The accurate prediction of F_(10.7) is of significant importance for short-term or long-term space weather forecasting.In this study,we apply Back Propagation(BP)neural network technique to forecast the daily F_(10.7)based on the trial data set of F_(10.7) from 1980 to 2001.Results show that this technique is better than the other prediction techniques for short-term forecasting,such as Support Vector Regression method.