A high‐performance belief propagation decoding algorithm for codes with short cycles

The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.     

基于置信传播的优化译码算法研究

该文在对LDPC码的译码算法分析的基础上,针对校验矩阵中含有的环对译码算法的影响,提出了一种在置信传播算法基础之上的译码算法。该算法通过及时切断消息在环上的重传回路,可消除因校验矩阵中的环回传原始信息对译码造成的影响,保证优质的原始信息能尽可能地传播到其能传播的节点,从而提升了LDPC码的译码性能。仿真实验表明,在低信噪比的信道中,该算法具有相当于传统算法的性能和更低的计算复杂度;在良好的信道条件下可以取得比传统算法更优异的性能。     

基于可靠性更新的低复杂度BP译码算法

基于部分符号更新策略的BP (Belief Propagation)译码算法减少了LDPC (Low-Density Parity-Check)码的译码运算量,提高了译码效率。然而在其译码过程中,由于变量节点可靠性判决准确率不高,而且可靠性被误判的错误节点无法在后继的译码中得到修正,译码性能大大降低。该文提出一种改进的节点可靠性判决准则,提高迭代过程中对变量节点可靠性判断的准确率;同时,在每次迭代结束后,重新衡量所有变量节点的可靠性,以此来消除可靠性误判对译码性能的影响。仿真结果表明,改进的算法不仅使传统BP译码的复杂度降低,而且提高了BP算法的译码性能。     

大距离徙动情况下距离多普勒(RD)算法与后向投影(BP)算法的比较

距离多普勒(Range-Doppler，RD)算法是传统窄带／窄波束SAR的经典成像算法，它借助菲涅耳近似，只保留了斜距R(t)的线性部分和二次项。但是当距离徙动严重时，方位向二次以上的高次相位项不能忽略，这会大大降低聚焦精度。后向投影(Back-Projection，BP)算法是一种基于时域处理的成像算法，通过计算双程延时将对应信号进行相干累加，获得高分辨率SAR图像。BP算法由于用时延代替了相位的概念，故与频率无关，不存在距离徙动校正的问题。本文介绍了RD算法和BP算法的原理及算法实现，并且利用距离向插值改进了BP算法。最后，结合计算机仿真结果详细比较了这两种算法的若干性能指标，证明了BP算法比RD算法更适用于大距离徙动情况下的SAR成像。     

Improving belief propagation on graphs with cycles

In this letter, we propose two modifications to belief propagation (BP) decoding algorithm. The modifications are based on reducing the reliability of messages throughout the iteration process, and are particularly effective for short low-density parity-check codes, where the existence of cycles makes the original BP algorithm perform suboptimal. The proposed algorithms, referred to as "normalized BP" and "offset BP," reduce the absolute value of the outgoing log-likelihood ratio messages at variable nodes by using a multiplicative factor and an additive factor, respectively. Simulation results show that both algorithms perform more or less the same, and both outperform BP in error performance.     

一种新型的卷积码混合译码算法

该文提出了一种级联的卷积码混合译码算法。该算法由两级译码实现,第1级采用置信传播(Belief-Propagation, BP)算法,而第2级采用修改的维特比译码(Modified Viterbi Decoding, MVD)算法。BP首先对接收序列进行预译码,并利用伴随式将译码输出的对数似然比值分为可靠的和不可靠的两类。不可靠的对数似然比值用接收符号取代,可靠的部分硬判决为编码符号,它们共同组成混合序列。随后,MVD对该混合序列作进一步纠错译码。仿真表明,与传统的维特比算法相比,所提出的混合译码算法的误码性能只有很小的损失,其译码平均复杂度在中高信噪比条件下有明显降低。     

一种改进的RA译码算法

重复累积(RA)码译码使用置信传播(BP)算法,具有接近香农限的性能,但校验节点更新时使用复杂的双曲正切函数和反双曲正切函数,算法复杂度较高。为了降低译码算法的复杂度,且具有较好的性能,该文将查表法和分段函数近似法结合起来,提出了一种改进的译码算法。该算法采用分段的一次函数,去近似BP算法检验节点变换化简后的原函数,采用非常小的查找表得到一个校正值,用校正值去修正近似函数和变换化简后的原函数之间的误差,很好地避免了复杂函数的计算,且误差极小。该算法大大降低了译码算法的复杂度,且具有接近BP算法的译码性能。     

一种结合比特翻转的自适应置信传播算法

提出了一种结合比特翻转的自适应置信传播迭代译码新算法,称之为"BP 比特翻转"算法.首先详细描述了新算法的整个流程,然后在相同仿真条件下比较了传统"BP"和"BP 比特翻转"两者的性能和平均迭代次数,发现新算法要优于传统的"BP"算法,特别是在最大迭代次数较小时,优势就会显得更加突出.     

Near optimum universal belief propagation based decoding oflow-density parity check codes

In this paper, we propose a belief-propagation (BP)-based decoding algorithm which utilizes normalization to improve the accuracy of the soft values delivered by a previously proposed simplified BP-based algorithm. The normalization factors can be obtained not only by simulation, but also, importantly, theoretically. This new BP-based algorithm is much simpler to implement than BP decoding as it requires only additions of the normalized received values and is universal, i.e., the decoding is independent of the channel characteristics. Some simulation results are given, which show this new decoding approach can achieve an error performance very close to that of BP on the additive white Gaussian noise channel, especially for low-density parity check (LDPC) codes whose check sums have large weights. The principle of normalization can also be used to improve the performance of the max-log-MAP algorithm in turbo decoding, and some coding gain can be achieved if the code length is long enough     

应用于40Gb/s DQPSK光通信系统的LDPC译码算法研究

针对40Gb/s差分正交相移键控(DQPSK)光通信传输系统,提出了低密度奇偶校验(low-density parity-check,LDPC)码译码算法的信息初始化公式,改进了基于置信度传播(belief propagation,BP)的译码算法,并进行了相应的数值仿真和性能分析比较,得到了兼顾性能和译码复杂度的改进型译码算法。     

一种改进的基于峰值信噪比-高阶奇异值分解的天波超视距雷达自适应海杂波抑制算法

天波超视距雷达(OTHR)舰船目标的检测性能受目标区海杂波的影响严重,准确且自适应的海杂波抑制效能对改善低可探测舰船目标的检测性能意义重大。该文针对基于高阶奇异值分解(HOSVD)的海杂波抑制算法非自适应机制的不足,通过引入峰值信噪比(PSNR),提出一种改进的基于PSNR-HOSVD的自适应算法。该算法仅利用第3等效模式展开矩阵的左奇异向量构造一个投影矩阵,相比于HOSVD算法,该文算法可有效降低计算复杂度,同时由于海杂波仅在第3等效模式展开矩阵的列空间中具有聚集特性,因此该文算法具有比HOSVD算法更好的海杂波抑制性能。实测数据处理结果表明,在电离层状态理想和非理想的情况下,该文PSNR-HOSVD自适应算法的性能均优于EVD自适应算法和HOSVD非自适应算法。     

基于误差反向传播算法的OFDM系统频域均衡

提出用一种基于神经网络的均衡方法,并用误差反向传播(BP)算法对多层前馈网络进行训练.分析和数值仿真结果表明,基于BP网络的频域均衡方法有较好的均衡效果,并且复杂度不高.     

一种基于归一化前景和角点信息的复杂场景人数统计方法

针对智能视频监控领域的人数统计问题,该文提出了一种基于归一化前景和角点信息的复杂场景人数统计方法。首先在提取的前景二值图基础上,计算透视校正后的归一化前景面积。然后在提取前景区域有效角点信息的基础上,计算能够反映人群遮挡程度的遮挡因子。最后,将上述两种特征输入后向传播(BP)网络完成人数统计算法的训练与测试。实验表明,该方法可以有效地实现对复杂场景的人数统计。     

系统RA码的基于WBF策略的改进BP译码算法

 针对重复累积(RA)码译码算法(BP算法和最小和算法)复杂度高或纠错性能下降的问题,将加权位翻转WBF的思想用于改进BP算法,提出了基于WBF策略的改进BP译码算法. 在每次迭代译码中若未能译出合法码字,则按一定规则进行位翻转操作,以期获得合法码字. 仿真结果表明,本算法能有效降低系统RA码的运算复杂度,且能保持优异的译码性能.     

前向多层神经网络模糊自适应算法

本文将模糊集理论与人工神经网络的研究相结合，提出一种模糊自适应ＢＰ算法，用典型异或问题与规模更大的打印机磁泄漏信息识别问题进行计算机模拟表明，该算法可使ＢＰ算法的收敛速度明显提高。此项工作为神经网络与模糊系统相结合探索了一条新的途径。     

IRA码最小和译码算法的改进算法

研究了重复累积(IRA)码的简化译码算法.IRA码的BP译码算法具有较高的复杂度,为了降低复杂度,首先提出将最小和算法应用于IRA码.然而,最小和算法使译码性能降低约1.2 dB.为了在复杂度和译码复杂度之间取得较好的折衷,提出了对IRA码的最小和算法的改进算法:归一化算法和偏移算法.仿真结果表明,IRA码归一化算法和偏移算法在复杂度略有增加的情况下,性能得到明显改善.     

改进Min-sum的LDPC译码算法研究

为了弥补Min-Sum译码算法相对于LLR-BP算法的性能缺陷,降低LLR-BP算法的实现复杂度,提出一种改进型Min-Sum译码算法,将Normalized BP-Based和Offset BP-Based 2种算法有效地结合,在计算校验节点消息时,同时引进校正因子和偏移因子,并通过最小均方差准则来选择参数。仿真结果表明,在误码率相同的条件下,改进型Min-Sum译码算法比Min-Sum算法、Normalized BP-Based算法和Offset BP-Based算法具有更好的译码性能,译码性能逼近于LLR-BP译码算法。     

Adaptive sparse system identification using normalized least mean fourth algorithm

Normalized least mean square (NLMS) was considered as one of the classical adaptive system identification algorithms. Because most of systems are often modeled as sparse, sparse NLMS algorithm was also applied to improve identification performance by taking the advantage of system sparsity. However, identification performances of NLMS type algorithms cannot achieve high‐identification performance, especially in low signal‐to‐noise ratio regime. It was well known that least mean fourth (LMF) can achieve high‐identification performance by utilizing fourth‐order identification error updating rather than second‐order. However, the main drawback of LMF is its instability and it cannot be applied to adaptive sparse system identifications. In this paper, we propose a stable sparse normalized LMF algorithm to exploit the sparse structure information to improve identification performance. Its stability is shown to be equivalent to sparse NLMS type algorithm. Simulation results show that the proposed normalized LMF algorithm can achieve better identification performance than sparse NLMS one. Copyright © 2013 John Wiley & Sons, Ltd.     

基于改进BP神经网络的数字识别

针对BP(Back Propagation)神经网络易陷入局部极小、收敛速度慢的缺点,提出了一种新的BP神经网络改进算法.与标准BP算法比较,该系统通过结合附加动量法和自适应学习速率形成新的BP改进算法.附加动量法虽然可以使BP算法避免陷入局部极小,但是对初始值的选取比较敏感,而且选取合适的学习速率比较困难.而自适应学...     

Variable non-uniform quantized belief propagation algorithm for LDPC decoding

Non-uniform quantization for messages in Low-Density Parity-Check（LDPC）decoding can reduce implementation complexity and mitigate performance loss.But the distribution of messages varies in the iterative decoding.This letter proposes a variable non-uniform quantized Belief Propagation（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 the unbiased estimation of variance,the distribution of messages can be tracked during the iteration.Thus the non-uniform quantization scheme can be optimized to minimize the distortion.Simulation results show that the variable non-uniform quantization scheme can achieve better error rate performance and faster decoding convergence than the conventional non-uniform quantization and uniform quantization schemes.