BP-based Algorithm Research Articles

Sequential Detection and Estimation of Multipath Channel Parameters Using Belief Propagation

This paper proposes a belief propagation (BP)-based algorithm for sequential detection and estimation of multipath component (MPC) parameters based on radio signals. Under dynamic channel conditions with moving transmitter/receiver, the number of MPCs, the MPC dispersion parameters, and the number of false alarm contributions are unknown and time-varying. We develop a Bayesian model for sequential detection and estimation of MPC dispersion parameters, and represent it by a factor graph enabling the use of BP for efficient computation of the marginal posterior distributions. At each time step, a snapshot-based parametric channel estimator provides parameter estimates of a set of MPCs which are used as noisy measurements by the proposed BP-based algorithm. It performs joint probabilistic data association, and estimation of the time-varying MPC parameters and the mean number of false alarm measurements, by means of the sum-product algorithm rules. The algorithm also exploits amplitude information enabling the reliable detection of "weak" MPCs with very low component signal-to-noise ratios (SNRs). The performance of the proposed algorithm compares well to state-of-the-art algorithms for high SNR MPCs, but it significantly outperforms them for medium or low SNR MPCs. Results using real radio measurements demonstrate the excellent performance of the proposed algorithm in realistic and challenging scenarios.

MAP-SNN: Mapping spike activities with multiplicity, adaptability, and plasticity into bio-plausible spiking neural networks.

Spiking Neural Networks (SNNs) are considered more biologically realistic and power-efficient as they imitate the fundamental mechanism of the human brain. Backpropagation (BP) based SNN learning algorithms that utilize deep learning frameworks have achieved good performance. However, those BP-based algorithms partially ignore bio-interpretability. In modeling spike activity for biological plausible BP-based SNNs, we examine three properties: multiplicity, adaptability, and plasticity (MAP). Regarding multiplicity, we propose a Multiple-Spike Pattern (MSP) with multiple-spike transmission to improve model robustness in discrete time iterations. To realize adaptability, we adopt Spike Frequency Adaption (SFA) under MSP to reduce spike activities for enhanced efficiency. For plasticity, we propose a trainable state-free synapse that models spike response current to increase the diversity of spiking neurons for temporal feature extraction. The proposed SNN model achieves competitive performances on the N-MNIST and SHD neuromorphic datasets. In addition, experimental results demonstrate that the proposed three aspects are significant to iterative robustness, spike efficiency, and the capacity to extract spikes' temporal features. In summary, this study presents a realistic approach for bio-inspired spike activity with MAP, presenting a novel neuromorphic perspective for incorporating biological properties into spiking neural networks.

An Enhanced Belief Propagation Flipping Decoder for Polar Codes with Stepping Strategy.

The Belief Propagation (BP) algorithm has the advantages of high-speed decoding and low latency. To improve the block error rate (BLER) performance of the BP-based algorithm, the BP flipping algorithm was proposed. However, the BP flipping algorithm attempts numerous useless flippings for improving the BLER performance. To reduce the number of decoding attempts needed without any loss of BLER performance, in this paper a metric is presented to evaluate the likelihood that the bits would correct the BP flipping decoding. Based on this, a BP-Step-Flipping (BPSF) algorithm is proposed which only traces the unreliable bits in the flip set (FS) to flip and skips over the reliable ones. In addition, a threshold is applied when the magnitude of the log–likelihood ratio (LLR) is small, and an enhanced BPSF (EBPSF) algorithm is presented to lower the BLER. With the same FS, the proposed algorithm can reduce the average number of iterations efficiently. Numerical results show the average number of iterations for EBPSF-1 decreases by 77.5% when N = 256, compared with the BP bit-flip-1 (BPF-1) algorithm at = 1.5 dB.

Multisensor-multitarget tracking based on belief propagation against false data injection attacks and denial of service attacks

This paper is concerned with the multisensor multitarget tracking where the sensor network can potentially be compromised by adversarial attacks, including false data injection (FDI) attacks and denial of service (DoS) attacks. We propose a multisensor multitarget tracking algorithm against FDI and DoS attacks based on belief propagation (BP) message passing method. With the factorization of joint posterior density, the statistical structure of the tracking problem is described by a factor graph. A BP-based algorithm is derived based on the factor graph for an efficient evaluation of the marginal posterior densities of the target states. The marginal posterior densities are then utilized for the detection and estimation of the multitarget states. Then, we develop an efficient Gaussian mixture implementation of the proposed BP-based algorithm for the linear Gaussian measurement and state evolution model. Simulation results illustrate that the proposed multisensor multitarget tracking algorithm can provide reliable tracking performance against FDI and DoS attacks.

Hybrid Multiagent Collaboration for Time-Critical Tasks: A Mathematical Model and Heuristic Approach

Principal–assistant agent teams are often employed to solve tasks in multiagent collaboration systems. Assistant agents attached to the principal agents are more flexible for task execution and can assist them to complete tasks with complex constraints. However, how to employ principal–assistant agent teams to execute time-critical tasks considering the dependency between agents and the constraints among tasks is still a challenge so far. In this paper, we investigate the principal–assistant collaboration problem with deadlines, which is to allocate tasks to suitable principal–assistant teams and construct routes satisfying the temporal constraints. Two cases are considered in this paper, including single principal–assistant teams and multiple principal–assistant teams. The former is formally formulated in an arc-based integer linear programming model. We develop a hybrid combination algorithm for adapting larger scales, the idea of which is to find an optimal combination of partial routes generated by heuristic methods. The latter is defined in a path-based integer linear programming model, and a branch-and-price-based (BP-based) algorithm is proposed that introduces the number of assistant-accessible tasks surrounding a task to guide the route construction. Experimental results validate that the hybrid combination algorithm and the BP-based algorithm are superior to the benchmarks in terms of the number of served tasks and the running time.

Fault diagnosis with synchrosqueezing transform and optimized deep convolutional neural network: An application in modular multilevel converters

High voltage direct current (HVDC) transmission mode with modular multilevel converters (MMC) topology is the future direction of transmission engineering, and security is their fundamental issue. Submodule fault of MMC in HVDC is the most common problem, nevertheless, traditional time–frequency based diagnosis technology can’t achieve high accuracy. To solve this pain spot, a new diagnosis strategy based on the synchrosqueezing transform (SST) and genetic algorithm optimized deep convolution neural network (GA-DCNN) is proposed in this paper. Firstly, the time–frequency representations (TFRs) of the raw signals which is synthesized by ac current and inner circulating current of the MMC are calculated with SST. Then, DCNN is introduced to learn the underlying features from the TFRs, and its key hyperparameters are optimized with genetic algorithm. Meanwhile, batch normalization, dropout and data augment technologies are explored to prevent DCNN model from overfitting and improve model performance. Compared to traditional SVM and BP-based algorithms, SST-GA-DCNN achieve high diagnosis accuracy. The experimental results show the feasibility and applicability of the proposed fault diagnosis framework.

Optimization and Hardware Implementation of Learning Assisted Min-Sum Decoders for Polar Codes

Polar codes have received a lot of attention due to their capacity-achieving performance and low complexity. This paper proposes a novel scaling offset min-sum (SOMS) algorithm and adapts the offset min-sum (OMS) algorithm for polar codes, and both algorithms are improved via learning. For all message updates, conventional min-sum decoding algorithms use the same scaling factor or offset, which is usually obtained by numerical simulations. By modeling the data flow of min-sum algorithms as a deep neural network, the parameters used in the message passing updates of min-sum decoders can be different for each message update, and are obtained by training and optimizing the corresponding deep neural network. The simulation results show that the proposed SOMS algorithm based on deep learning performs better than all existing BP-based algorithms. Moreover, this paper presents an efficient hardware architecture of the proposed SOMS algorithm. The K-Means clustering algorithm is applied to reduce the number of possible parameters of the neural network, leading to reduced energy consumption and memory requirement with negligible error performance degradation. The proposed architecture of the SOMS algorithm for a (256,128) polar code is implemented and validated on the Xilinx Artix-7 field-programmable gate array.

Design and Analysis of a UWB MIMO Radar System with Miniaturized Vivaldi Antenna for Through-Wall Imaging

The ultra-wideband (UWB) multi-input multi-output (MIMO) radar technique is playing a more and more important role in the application of through-wall detection because of its high resolution, lower antenna requirements, and efficient data capturing ability. This paper develops a novel UWB MIMO radar system using a stepped-frequency continuous-wave (SFCW) signal, which is designed to detect human targets behind the regular brick and concrete wall. In order to balance high range resolution and wall-penetration depth, a novel miniaturized Vivaldi antenna with desired bandwidth of 0.5–2.5 GHz was designed, simulated, manufactured, and successfully used in through-wall imaging. To suppress the artifacts in the focused image and reduce the computing complexity, the cross-correlation-based time domain back projection (CC-TDBP) algorithm was developed. In addition, a through-wall imaging model was established, based on which the effects of the wall on the refraction of electromagnetic (EM) waves and the reduction of velocity are compensated. Finally, different experiments were conducted for multiple stationary targets utilizing the designed radar system, and the improved BP-based algorithms are applied to focus the targets behind the wall more accurately. The reconstructed two-dimensional (2D) images illustrate that the designed MIMO radar system can successfully detect and image human targets in the air and behind the wall.

A Scalable Algorithm for Network Localization and Synchronization

The Internet of Things (IoT) will seamlessly integrate a large number of densely deployed heterogeneous devices and will enable new location-aware services. However, fine-grained localization of IoT devices is challenging as their computation and communication resources are typically limited and different devices may have different qualities of internal clocks and different mobility patterns. To address these challenges, we propose a cooperative, scalable, and time-recursive algorithm for network localization and synchronization (NLS). Our algorithm is based on time measurements and supports heterogeneous devices with limited computation and communication resources, time-varying clock and location parameters, arbitrary state-evolution models, and time-varying network connectivity. These attributes make the proposed algorithm attractive for IoT-related applications. The algorithm is furthermore able to incorporate measurements from additional sensors for positioning, navigation, and timing such as receivers for global navigation satellite systems. Based on a factor graph representation of the underlying spatiotemporal Bayesian sequential estimation problem, the algorithm uses belief propagation (BP) for an efficient marginalization of the joint posterior distribution. To account for the nonlinear measurement model and nonlinear state-evolution models while keeping the communication and computation requirements low, we develop an efficient second-order implementation of the BP rules by means of the recently introduced sigma point belief propagation technique. Simulation results demonstrate the high synchronization and localization accuracy as well as the low computational complexity of the proposed algorithm. In particular, in sufficiently dense networks, the proposed algorithm outperforms the state-of-the-art BP-based algorithm for NLS in terms of both estimation accuracy and computational complexity.

Reduced-Complexity Decoding of LT Codes

In this paper, the belief propagation (BP) based approximation methods for low-density parity-check codes are adapted to the Luby transform soft decoder structure in order to reduce its computational complexity. Moreover, the log-likelihood ratio based adaptive demodulation algorithm is combined with the BP and BP-based algorithms to further reduce the computational complexities and optimum key parameters are determined for normalized min-sum and offset min-sum algorithms. The bit error rate performances of the algorithms over the binary input additive white Gaussian noise channel are obtained by both theoretically and simulations. For theoretical analysis, the Monte-Carlo based density evolution method is used. In addition, computational complexity analyzes of methods are presented. Results show that the computational complexity can be reduced significantly by using combined methods which cost limited signal to noise ratio loss.

Analysis of the Min-Sum Algorithm for Packing and Covering Problems via Linear Programming

Message-passing algorithms based on belief-propagation (BP) are successfully used in many applications, including decoding error correcting codes and solving constraint satisfaction and inference problems. The BP-based algorithms operate over graph representations, called factor graphs, that are used to model the input. Although in many cases, the BP-based algorithms exhibit impressive empirical results, not much has been proved when the factor graphs have cycles. This paper deals with packing and covering integer programs in which the constraint matrix is zero-one, the constraint vector is integral, and the variables are subject to box constraints. We study the performance of the min-sum algorithm when applied to the corresponding factor graph models of packing and covering linear programmings (LPs). We compare the solutions computed by the min-sum algorithm for packing and covering problems to the optimal solutions of the corresponding LP relaxations. In particular, we prove that if the LP has an optimal fractional solution, then for each fractional component, the min-sum algorithm either computes multiple solutions or the solution oscillates below and above the fraction. This implies that the min-sum algorithm computes the optimal integral solution only if the LP has a unique optimal solution that is integral. The converse is not true in general. For a special case of packing and covering problems, we prove that if the LP has a unique optimal solution that is integral and on the boundary of the box constraints, then the min-sum algorithm computes the optimal solution in pseudopolynomial time. Our results unify and extend recent results for the maximum weight matching problem and for the maximum weight independent set problem.

Improvement of LDPC Codes Decoding Algorithm in the Application of the Rotational OFDM System

Because the performance of LDPC codes is better than Turbo codes, convolution codes, etc., so the combination of LDPC codes and the OFDM technology has higher effectiveness. Traditional LDPC decoding algorithm (BP algorithm) exists large amounts of multiplication, division and index calculation, and when decoding cycle, its computational cost will increase exponentially, which not only increases the complexity, and makes the numerical stability of the algorithm deteriorates, therefore, in this paper, we propose an improved decoding algorithm, namely the combination algorithm of Offset-BP-base and Offset BP. In the AWGN channel environment and the rotational modulation of OFDM, compared with LLR BP algorithm and BP-based algorithm, the improved algorithm improves the performance of the system, and the complexity is reduced.

Image segmentation based on hierarchical belief propagation with variable weighting parameters

The belief propagation (BP) algorithm is an efficient way to minimize the MRF energy for image segmentation. This paper proposes a hierarchical BP algorithm with variable weighting parameters (HBP-VW) to improve the segmentation accuracy of the BP-based algorithms. In the HBP-VW, two variable weighting parameters are introduced, the global parameter and the local parameter. The global parameter is used to overall adjust the influence of each part in the message update rule. The local parameter is designed to describe the local texture pattern for each site. Texture, remote sensing, and nature images are employed to test the proposed algorithm. Experimental results illustrate a better segmentation accuracy compared with other BP-based algorithms.

A Classified Normalized BP-Based Algorithm with 2-Dimensional Correction for LDPC Codes

A BP-based algorithm with 2-dimensional classified normalized correction is developed to reduce the complexity and improve the performance of decoding algorithm for the low density parity check (LDPC) codes. The algorithm first utilizes classification according to the absolute values of incoming messages in check nodes. Then it uses 2-dimensional normalization to correct the minimum and sub-minimum values. The 2-dimensional normalized factors can be calculated respectively by using probability and statistic theory in the initialization step. Simulation results illustrate that the proposed algorithm achieves better performance in bit error ratio (BER) and average iteration number than normalized BP-based algorithm in the high signal noise ratio (SNR) region, i.e., it can achieve 0.4 dB SNR gain and reduce 20% number of iterations at BER= 5 10  , whose complexity is also much less than that of belief propagation (BP) algorithm. It is concluded that the proposed algorithm offers better tradeoff between performance and complexity.  Index Terms—channel coding theory, density evolution, Iterative decoding algorithm

Applications of Belief Propagation in CSMA Wireless Networks

Belief propagation (BP) is an efficient way to solve inference problems in graphical models, such as Bayesian networks and Markov random fields. It has found great success in many application areas due to its simplicity, high accuracy, and distributed nature. This paper is a first attempt to apply BP algorithms in CSMA wireless networks. Compared to prior CSMA optimization algorithms such as ACSMA, which are measurement-based, BP-based algorithms are proactive and computational, without the need for network probing and traffic measurement. Consequently, BP-based algorithms are not affected by the temporal throughput fluctuations and can converge faster. Specifically, this paper explores three applications of BP. 1) We show how BP can be used to compute the throughputs of different links in the network given their access intensities, defined as the mean packet transmission time divided by the mean backoff countdown time. 2) We propose an inverse-BP algorithm to solve the reverse problem of how to set the access intensities of different links to meet their target throughputs. 3) We introduce a BP-adaptive CSMA algorithm to find the link access intensities that can achieve optimal system utility. The first two applications are NP-hard problems, and BP provides good approximations to them. The advantage of BP is that it can converge faster compared to prior algorithms like ACSMA, especially in CSMA networks with temporal throughput fluctuations. Furthermore, this paper goes beyond BP and considers a generalized version of it, GBP, to improve accuracy in networks with a loopy contention graph. The distributed implementation of GBP is nontrivial to construct. A contribution of this paper is to show that a maximal clique method of forming regions in GBP: 1) yields accurate results; and 2) is amenable to distributed implementation in CSMA networks, with messages passed between one-hop neighbors only. We show that both BP and GBP algorithms for all three applications can yield solutions within seconds in real operation.

基于MMSE的大气激光通信中LDPC码BP译码算法研究

Due to high complexity of Belief Propagation(BP) algorithm,several kind of BP-based simplified decoding algorithms are analyzed.Based on the Minimum Mean Square Erro(MMSE) criterion,optimal design of the scaled BP-based and offset BP-based algorithms is discussed.The theoretical formulas and numerical calculations on the optimal factors for these two BP-based algorithms are provdied.The simualtion resutls for the(6,3)regualr LDPC codes of lengths 1008 on the weak atmospheric turbulence channel demonstrate that the scaeld BP-based and offset BP-based aglorithms with the proposed factors are better than Min-Sum Algorithm,and even can achieve the performance better than that of the BP algorithm,and have lower complexity compared with BP algortihm.

Performance Analysis of MIA Algorithm for LDPC Codes in near Space Rain Attenuation Channel

According to the influence of grand reflector to the channel, near space Ka-band rain attenuation channel model of area coverage is improved. According to RRWBF algorithm and UMP BP-Based algorithm of LDPC codes, a mixed iterative decoding algorithm is proposed. The algorithm takes advantage of low complexity of hard-decision algorithm and high performance of soft-decision algorithm, so in near space rain attenuation channel, the decoding complexity significantly reduced when bit error rate performance does not decline. Simulation results show that in near space rain attenuation channel, MIA algorithm can reduce decoding complexity by about 30%, compare with the UMP BP-Based algorithm.

Belief Propagation for Error Correcting Codes and Lossy Compression Using Multilayer Perceptrons

The belief propagation (BP) based algorithm is investigated as a potential decoder for both of error correcting codes and lossy compression, which are based on non-monotonic tree-like multilayer perceptron encoders. We discuss that whether the BP can give practical algorithms or not in these schemes. The BP implementations in those kind of fully connected networks unfortunately shows strong limitation, while the theoretical results seems a bit promising. Instead, it reveals it might have a rich and complex structure of the solution space via the BP-based algorithms.

Magnetization Performance of LDPC Reduced-Complexity Decoding Algorithms

Low-density parity-check (LDPC) codes are very efficient for communicating reliably through a noisy channel. N.Sourlas [1] showed that LDPC codes, which revolutionize the codes domain and used in many communications standards, can be mapped onto an Ising spin systems. Besides, it has been shown that the Belief-Propagation (BP) algorithm, the LDPC codes decoding algorithm, is equivalent to the Thouless- Anderson-Palmer (TAP) approach [2]. Unfortunately, no study has been made for the other decoding algorithms. In this paper, we develop the Log-Likelihood Ratios-Belief Propagation (LLR-BP) algorithm and its simplifications the BP-Based algorithm and the λ-min algorithm with the TAP approach. We present the performance of these decoding algorithms using statistical physics argument i.e., we present the performance as function of the magnetization.

Self-adjustable offset min-sum algorithm for ISDB-S2 LDPC decoder

In this paper, a novel self-adjustable offset min-sum LDPC decoding algorithm is proposed for ISDB-S2 application. We present for the first time a uniform approximation of the check node operation through mathematical induction on Jacobian logarithm and theoretically shows that the offset value is mainly dependent on the difference of the two most unreliable inputs from the bit nodes, which makes the offset value adjustable during the iterative decoding procedure. Simulation results for all 11 code rates of ISDB-S2 demonstrate that the proposed method can achieve an average of 0.15dB gain compared to the Min-sum based algorithms, and consumes only 1.21% computation complexity compared to BP-based algorithms in the best case.