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.

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.

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.

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.

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.

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。

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。

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.

3×3核矩阵极化码的BP译码算法

相比于2×2核极化码,3×3核极化码的码长更加丰富以及有着更高的极化速率。同时,极化码的置信传播(Belief Propagation, BP)算法相比于传统串行消去(Successive Cancellation, SC)译码算法具有更低的延时。将2×2核极化码的BP译码算法推广至3×3核。获得了3×3核内部最小计算单元的信息更新公式;基于信息更新公式,给出了3×3核的BP译码算法。仿真结果表明,对于3×3核极化码,BP译码算法相比于SC译码算法,在中低信噪比下性能要优于SC译码算法。在译码性能相当的条件下,BP译码算法有着更低的译码延时。

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.

基于BSO-BP的船舶油耗预测模型

为解决基于传统反向传播(back propagation,BP)神经网络的船舶油耗预测模型易陷入极小值和误差较大的问题,提出一种利用头脑风暴优化(brain storm optimization,BSO)算法优化BP神经网络的船舶油耗预测模型(简称BSO-BP模型)。以“维多利亚凯娅”号内河游船为研究对象,将BSO-BP模型的预测结果与采用传统BP神经网络以及模拟退火(simulated annealing,SA)算法、遗传算法(genetic algorithm,GA)、粒子群优化(particle swarm optimization,PSO)算法优化的BP神经网络的船舶油耗预测模型的预测结果进行对比分析。结果表明:与传统BP神经网络模型的预测结果相比,BSO-BP模型预测结果的可决系数R^(2)提高了0.003 9,均方误差、均方根误差、平均相对误差、平均绝对误差分别降低了0.034 4、0.154 1、0.010 2、0.017 8,说明在船舶油耗预测中BSO算法对BP神经网络的预测精度有显著的提升作用;BSO-BP模型预测结果的各项评价指标在所对比的5种模型中均表现最好,说明与SA算法、GA和PSO算法相比,BSO算法对BP神经网络的提升效果更好。

基于BP神经网络的上海生鲜农产品物流需求预测

针对传统的生鲜农产品物流非线性需求预测模型收敛速度慢、精度低等问题,构建由改进粒子群(improved particle swarm optimization,IPSO)算法优化反向传播(back propagation,BP)神经网络的预测模型。引入对立学习机制、自适应惯性权重、非对称学习因子提升粒子群(particle swarm optimization,PSO)算法的初始解质量,平衡算法的局部开发和全局搜索能力;利用IPSO算法优化BP神经网络的权值和阈值,解决BP神经网络收敛速度慢、容易陷入局部最优等问题。通过上海生鲜农产品物流需求预测实例对模型的有效性进行验证,结果显示:IPSO-BP神经网络模型在预测精度及收敛速度上均明显优于传统PSO-BP神经网络和BP神经网络模型。

基于BP神经网络的谐波减速器柔轮疲劳寿命预测研究

柔轮是谐波减速器的易损零件,在波发生器的高转速带动下转动,其疲劳寿命一直是备受关注的研究重点。以某型号杯型谐波减速器柔轮为研究对象,建立有限元仿真模型,得到柔轮最大应力与筒长、筒体壁厚和不同过渡圆角半径等参数之间的关系。根据柔轮S-N曲线,计算得到柔轮疲劳寿命,利用反向传播(Back Propagation,BP)神经网络实现了柔轮疲劳寿命的预测。

一种LM-BP加速搜索的周跳探测与修复方法

针对传统三频周跳探测与修复方法中的不敏感、漏检以及效率较低等问题,提出一种基于莱文伯格-马夸特(LM)-反向传播(BP)神经网络加速搜索法的伪距相位组合与电离层残差组合联合周跳探测与修复方法:利用2个伪距相位组合以减少不敏感周跳数量,利用1个电离层残差组合以提高小周跳探测敏感度;在构成3个线性无关的组合观测值后,使用LM-BP加速搜索算法进行周跳探测与修复。实验结果表明,相对常规的伪距相位组合与电离层残差组合联合方法,该方法能够提高周跳探测与修复性能,可探测小至1个的周跳,探测与修复整体时效有较大提升。

基于煤岩煤质多元指标的BP神经网络焦油产率预测方法研究

【目的】焦油产率是煤低温干馏利用最重要的煤质参数,决定着富油煤的清洁利用方向。但由于多方面的原因,在煤炭地质勘查阶段对煤焦油产率的测试数据十分有限,极大地制约了富油煤的精细评价和高效利用。【方法】为了提高富油煤精细评价的科学性和准确性,以陕北侏罗纪煤田以往测试1073组煤岩煤质数据为基础,并筛选出显微组分、工业分析、元素分析、灰成分分析等20项煤岩煤质参数齐全的141组数据,利用BP神经网络算法分别建立了20项煤岩煤质指标的焦油产率预测模型和以4项工业分析为基础的焦油产率预测模型,并对预测模型的准确性和合理性进行分析评价。【结果和结论】结果表明:以20项煤岩煤质指标为特征建立的预测模型最终训练均方误差为0.30,测试集数据预测结果平均绝对误差为0.65;以4项工业分析指标为特征建立的预测模型最终训练均方误差为1.07,测试集数据预测结果平均绝对误差为1.35;扩展集数据在两个模型中预测结果平均绝对误差分别为0.84和1.34,显示出20项煤岩煤质指标比4项工业分析煤质指标建立的预测模型具有更高的拟合优度和泛化性能。利用SHAP算法进一步对预测模型中20项煤岩煤质指标的重要性进行量化分析,显示出镜质组、氢元素、三氧化二铁、水分、挥发分、碳元素、壳质组、氧元素含量是焦油产率的正向影响因素,三氧化二铝、惰质组、固定碳、灰分、二氧化硅含量是焦油产率的负向影响因素,模型中煤岩煤质与焦油产率之间的内在联系很好地契合了地质上对焦油产率影响因素的基本认识,该焦油产率预测模型可以很好地应用于陕北侏罗纪煤田的焦油产率预测,为陕北地区富油煤的清洁高效利用提供支撑。

基于MFO-BP算法的移动机器人定位研究

针对移动机器人定位问题,以自主搭建的复合式机器人为基础,提出一种基于飞蛾火焰优化-反向传播(MFO-BP)算法的移动机器人定位预测方法。将移动机器人视为一个“黑箱”,不单独考虑系统和非系统误差的影响,输入理论坐标值,输出预测坐标值。试验结果表明,MFO-BP算法预测模型能有效进行移动机器人定位预测,并且精度远高于传统反向传播(BP)神经网络预测模型。为了验证模型结构对预测结果的影响,将MFO-BP算法预测模型分为单隐含层和双隐含层这两种。试验结果显示,MFO-BP算法双隐含层与单隐含层相比,前者平均绝对误差更小、误差波动范围也更小、预测误差趋势更平稳。MFO-BP算法双隐含层预测效果更优,可以应用于复合式机器人末端定位。