Belief Propagation Algorithm Research Articles

A closer look at the belief propagation algorithm in side-channel attack on CCA-secure PQC KEM

A closer look at the belief propagation algorithm in side-channel attack on CCA-secure PQC KEM

Counting the number of solutions in satisfiability problems with tensor-network message passing.

We investigate how to count the number of solutions in the Boolean satisfiability (SAT) problem, a fundamental problem in theoretical computer science that has applications in various domains. We convert the problem to a spin-glass problem in statistical physics and approximately compute the entropy of the problem, which corresponds to the logarithm of the number of solutions. We propose a new method for the entropy computing problem based on a combination of the tensor network method and the message-passing algorithm. The significance of the proposed method is its ability to consider the effects of both long loops and short loops present in the factor graph of the SAT problem. We validate the efficacy of our approach using 3-SAT problems defined on the random graphs and structured graphs, and show that the proposed method gives more accurate results on the number of solutions than the standard belief propagation algorithms. We also discuss the applications of our method across a wide range of combinatorial optimization problems.

A Low-Density Parity-Check Coding Scheme for LoRa Networking

This article presents a novel system, LLDPC , 1 which brings Low-Density Parity-Check (LDPC) codes into Long Range (LoRa) networks to improve Forward Error Correction, a task currently managed by less efficient Hamming codes. Three challenges in achieving this are addressed: First, Chirp Spread Spectrum (CSS) modulation used by LoRa produces only hard demodulation outcomes, whereas LDPC decoding requires Log-Likelihood Ratios (LLR) for each bit. We solve this by developing a CSS-specific LLR extractor. Second, we improve LDPC decoding efficiency by using symbol-level information to fine-tune LLRs of error-prone bits. Finally, to minimize the decoding latency caused by the computationally heavy Soft Belief Propagation (SBP) algorithm typically used in LDPC decoding, we apply graph neural networks to accelerate the process. Our results show that LLDPC extends default LoRa’s lifetime by 86.7% and reduces SBP algorithm decoding latency by 58.09×.

Multi-sensor multi-target tracking with generalized labeled multi-Bernoulli filter based on track-before-detect observation model using Gaussian belief propagation

Tracking an unknown number of low-observable targets is notoriously challenging problem. This paper extends the multi-sensor multi-target tracking with generalized labeled multi-Bernoulli (GLMB) filter into the track-before-detect (TBD) observation model and presents its efficient implementation. The Gaussian belief propagation (BP) is applied into multi-sensor GLMB-TBD filter to address the computational bottleneck of computing GLMB filtering density for tracking multiple targets in challenging scenario. The Gaussian BP algorithm is used to directly compute marginal densities from the joint posterior density through the BP belief update wherein the GLMB filtering density at given time serves as prior information for next recursion. Compared to the Gibbs sampling-version implementation, the Gaussian BP-version implementation avoids the pruning of GLMB components without association information loss and the relevant association is preserved for BP belief update. Hence, the proposed Gaussian BP-version implementation can improve the tracking accuracy. Moreover, the computational complexity of our proposed Gaussian BP-version implementation scales linear complexity in the total number of measurements from all sensors. More importantly, the linear scaling in number of Bernoulli components for our proposed Gaussian BP-version implementation improves on the quadratic complexity exhibited by the Gibbs-version one. The experiment results show that the computational cost of the Gaussian BP-version implementation is significantly less than that of the Gibbs sampling-version implementation for the multi-sensor GLMB-TBD filter.

Distributed angle‐only orbit determination algorithm for non‐cooperative spacecraft based on factor graph

AbstractBayesian filtering provides an effective approach for the orbit determination of a non‐cooperative target using angle measurements from multiple CubeSats. However, existing methods face challenges such as low reliability and limited estimation accuracy. Two distributed filtering algorithms based on factor graphs employed in the sub‐parent and distributed cluster spacecraft architectures are proposed. Two appropriate factor graphs representing different cluster spacecraft structures are designed and implement distributed Bayesian filtering within these models. The Gaussian messages transmitted between nodes and the probability distributions of variable nodes are calculated using the derived non‐linear Gaussian belief propagation algorithm. Gaussian messages propagate from the deputy spacecraft to the chief spacecraft in the sub‐parent spacecraft architecture, demonstrating that the estimation accuracy converges to the centralised extended Kalman filter (EKF). Simulation results indicate that the algorithm enhances system robustness in observation node failures without compromising accuracy. In the distributed spacecraft architecture, neighbouring spacecraft iteratively exchanges Gaussian messages. The accuracy of the algorithm can rapidly approach the centralised EKF, benefiting from the efficient and unbiased transmission of observational information. Compared to existing distributed consensus filtering algorithms, the proposed algorithm improves estimation accuracy and reduces the number of iterations needed to achieve consensus.

DNBP: Differentiable Nonparametric Belief Propagation

We present a differentiable approach to learn the probabilistic factors used for inference by a nonparametric belief propagation algorithm. Existing nonparametric belief propagation methods rely on domain-specific features encoded in the probabilistic factors of a graphical model. In this work, we replace each crafted factor with a differentiable neural network, enabling the factors to be learned using an efficient optimization routine from labeled data. By combining differentiable neural networks with an efficient belief propagation algorithm, our method learns to maintain a set of marginal posterior samples using end-to-end training. We evaluate our differentiable nonparametric belief propagation (DNBP) method on a set of articulated pose tracking tasks and compare performance with learned baselines. Results from these experiments demonstrate the effectiveness of using learned factors for tracking and suggest the practical advantage over hand-crafted approaches. The project webpage is available at: https://progress.eecs.umich.edu/projects/dnbp/ .

基于边际概率分布重新进行单变量选取的置信传播算法求解约束满足问题

基于边际概率分布重新进行单变量选取的置信传播算法求解约束满足问题

Research on the Era Value and Communication Path of Human Destiny Community and Socialist Core Values in the Context of Big Data

Abstract This paper analyzes the socialist core values and explores the contemporary characteristics and values of socialist core values under the background of big data. On this basis, in order to better practice the socialist core values, through the communication path of big data, combined with the belief propagation algorithm and the association effect, it constructs a node influence propagation NIP model based on the improvement of knowledge graph to realize the propagation of socialist core values. At the same time, the algorithm constructed in this paper is subjected to performance verification experiments, and the effect of socialist core value dissemination and the value of the times are explored. The results show that the influence range of the national level and the individual level are roughly the same as 1200 and 1190, respectively, both slightly higher than the individual influence range of 1000, and the propagation time of the state, society and individual is within 150s, 200s and 300s respectively. Resistance to Western ideology rose by 0.13, the deepening of socialist theory grew by 0.09, and the process of constructing a world value system increased by 0.06. Based on this paper, the study of the value of time and the path of dissemination has a positive impact on the development of socialism.

Partial IDS decoding based on the base graph of protograph LDPC codes

AbstractThe residual belief propagation (RBP) algorithm, which is the most classic informed dynamic scheduling strategy, achieves outstanding performance in error correction and can drastically accelerate convergence speed. However, the greedy algorithmic property of this iterative decoding will inevitably cause loss of decoding performance. To address this, a novel algorithm called the partial average bundle residual belief propagation (PABRBP) is proposed in this paper. According to the construction characteristics of a base matrix of protograph‐LDPC codes, informed dynamic scheduling (IDS) strategies are applied to an edge bundle of base matrices for the first time. This edge bundle of the base matrix can be applied to a corresponding cyclic permutation matrix. Furthermore, the update level of each bundle is determined by the value of the Partially Average Bundle Residual (PABR). Therefore, the edge message with the maximum residual in each bundle is updated in order, and the process of iterative decoding is less likely to become trapped in a local optimum. Additionally, the generation of silent nodes is reduced as much as possible. To further improve the PABRBP decoding performance for medium and long codes over the fading channel, the adjusted compensation term is periodically introduced. Analysis and simulation results show that PABRBP demonstrates a notable convergence quality and decoding performance improvement over the fading channels compared to existing state‐of‐art IDS algorithms.

Distributed Inference Over Linear Models Using Alternating Gaussian Belief Propagation

We consider the problem of maximum likelihood estimation in linear models represented by factor graphs and solved via the Gaussian belief propagation algorithm. Motivated by massive internet of things (IoT) networks and edge computing, we set the above problem in a clustered scenario, where the factor graph is divided into clusters and assigned for processing in a distributed fashion across a number of edge computing nodes. For these scenarios, we show that an alternating Gaussian belief propagation (AGBP) algorithm that alternates between inter-and intra-cluster iterations, demonstrates superior performance in terms of convergence properties compared to the existing solutions in the literature. We present a comprehensive framework and introduce appropriate metrics to analyse AGBP algorithm across a wide range of linear models characterised by symmetric and non-symmetric, square, and rectangular matrices. We extend the analysis to the case of dynamic linear models by introducing dynamic arrival of new data over time. Using a combination of analytical and extensive numerical results, we show the efficiency and scalability of AGBP algorithm, making it a suitable solution for large-scale inference in massive IoT networks.

Deep-Learning-Based Adaptive Error-Correction Decoding for Spin-Torque Transfer Magnetic Random Access Memory (STT-MRAM)

Spin-torque transfer magnetic random access memory (STT-MRAM) is a promising emerging non-volatile memory (NVM) technology with wide applications. However, the data recovery of STT-MRAM is affected by the diversity of channel raw bit error rate (BER) across different dies caused by process variations, as well as the unknown resistance offset due to temperature change. Therefore, it is critical to develop effective decoding algorithms of error correction codes for STT-MRAM. In this paper, we first propose a neural bit-flipping (BF) decoding algorithm, which can share the same trellis representation as the state-of-the-art neural decoding algorithms, such as the neural belief propagation (NBP) and neural offset min-sum (NOMS) algorithm. Hence a neural network (NN) decoder with a uniform architecture but different NN parameters can realize all these neural decoding algorithms. Based on such a unified NN decoder architecture, we further propose a novel deep learning (DL)-based adaptive decoding algorithm whose decoding complexity can be adjusted according to the change of the channel conditions of STT-MRAM. Extensive experimental evaluation results demonstrate that the proposed neural decoders can greatly improve the performance over the standard decoders, with similar decoding latency and energy consumption. Moreover, the DL-based adaptive decoder can work well over different channel conditions of STT-MRAM irrespective of the unknown resistance offset, with a 50% reduction of the decoding latency and energy consumption compared to the fixed decoder.

Analysis of film distribution methods based on artificial intelligence technology

Abstract In this paper, we first sort out the common film communication media and film communication methods and explore the application of visual language and multimodal discourse analysis based on artificial intelligence in film communication. Then, the maximum flow belief propagation algorithm is designed by combining the belief algorithm based on the information propagation algorithm with the maximum flow linear programming equation, and the minimum cost of movie propagation methods based on artificial intelligence technology is designed. Finally, the accuracy, speed, and cost of the movie dissemination method using AI technology are analyzed by the MovieLens dataset. The results show that this dissemination method has the lowest MAE and RMSE values of 0.79 and 0.82, respectively, and the minimum average cost is 0.38 per person, which can be effectively disseminated.

Cooperative localization for master–salve multi-AUVs based on range measurements

Underwater localization has consistently remained a prominent technical challenge for autonomous underwater vehicles (AUVs). The advent of cooperative localization techniques has emerged as a novel avenue for enhancing localization accuracy. The master–slave cooperative localization mode has gained widespread adoption due to its cost-effectiveness in implementation. In view of the complexity of underwater noise characteristics, in the multi-AUVs cooperative localization system, this paper addresses scenarios involving distance-dependent noise in a master–slave-based multi-AUVs cooperative localization system. To tackle the negative impact of distance-dependent noise and the non-linearity of the distance function, a two-step algorithm is proposed that combines maximum likelihood estimation and the Gaussian belief propagation algorithm (ML-GBP) to estimate the positions of AUVs. The maximum likelihood estimation is employed to cope with the interference caused by distance-dependent noise, and subsequently, the Gaussian belief propagation algorithm, based on range observations and reference information, is used to achieve accurate estimation of AUV positions and implement position correction. Simulation results demonstrate that the proposed ML-GBP algorithm outperforms traditional extended Kalman filter (EKF) and nonparametric belief propagation (NBP) methods by enhancing the localization accuracy of the system while exhibiting superior performance in terms of computational complexity and system communication overhead.

Belief Propagation Optimization for Lossy Compression Based on Gaussian Source

In the Internet of Things, sensor nodes collect environmental information and utilize lossy compression for saving storage space. To achieve this objective, high-efficiency compression of the continuous source should be studied. Different from existing schemes, lossy source coding is implemented based on the duality principle in this work. Referring to the duality principle between the lossy source coding and the channel decoding, the belief propagation (BP) algorithm is introduced to realize lossy compression based on a Gaussian source. In the BP algorithm, the log-likelihood ratios (LLRs) are iterated, and their iteration paths follow the connecting relation between the check nodes and the variable nodes in the protograph low-density parity-check (P-LDPC) code. During LLR iterations, the trapping set is the main factor that influences compression performance. We propose the optimized BP algorithms to weaken the impact of trapping sets. The simulation results indicate that the optimized BP algorithms obtain better distortion–rate performance.

Improved adaptive belief propagation algorithm with reduced complexity for concatenated SPC‐RS codes

AbstractIn this letter, a novel single parity check‐aided minimum sum (SPC‐aided MS) algorithm is proposed. A cascaded compiled code scheme is used to approximate the adaptive belief propagation (ABP) algorithm for Reed–Solomon (RS) codes using the min sum (MS) algorithm. The computational complexity is greatly reduced compared with the previous algorithm. Simulation results show that the SPC‐aided MS algorithm can achieve coding gains of up to 1.1, 0.7, and 0.6 dB for RS (255,239) code compared with the conventional ABP, LRBP, and HD‐P‐ABP algorithms, respectively under the condition of .

An intelligent workflow for sub-nanoscale 3D reconstruction of intact synapses from serial section electron tomography

BackgroundAs an extension of electron tomography (ET), serial section electron tomography (serial section ET) aims to align the tomographic images of multiple thick tissue sections together, to break through the volume limitation of the single section and preserve the sub-nanoscale voxel size. It could be applied to reconstruct the intact synapse, which expands about one micrometer and contains nanoscale vesicles. However, there are several drawbacks of the existing serial section ET methods. First, locating and imaging regions of interest (ROIs) in serial sections during the shooting process is time-consuming. Second, the alignment of ET volumes is difficult due to the missing information caused by section cutting and imaging. Here we report a workflow to simplify the acquisition of ROIs in serial sections, automatically align the volume of serial section ET, and semi-automatically reconstruct the target synaptic structure.ResultsWe propose an intelligent workflow to reconstruct the intact synapse with sub-nanometer voxel size. Our workflow includes rapid localization of ROIs in serial sections, automatic alignment, restoration, assembly of serial ET volumes, and semi-automatic target structure segmentation. For the localization and acquisition of ROIs in serial sections, we use affine transformations to calculate their approximate position based on their relative location in orderly placed sections. For the alignment of consecutive ET volumes with significantly distinct appearances, we use multi-scale image feature matching and the elastic with belief propagation (BP-Elastic) algorithm to align them from coarse to fine. For the restoration of the missing information in ET, we first estimate the number of lost images based on the pixel changes of adjacent volumes after alignment. Then, we present a missing information generation network that is appropriate for small-sample of ET volume using pre-training interpolation network and distillation learning. And we use it to generate the missing information to achieve the whole volume reconstruction. For the reconstruction of synaptic ultrastructures, we use a 3D neural network to obtain them quickly. In summary, our workflow can quickly locate and acquire ROIs in serial sections, automatically align, restore, assemble serial sections, and obtain the complete segmentation result of the target structure with minimal manual manipulation. Multiple intact synapses in wild-type rat were reconstructed at a voxel size of 0.664 nm/voxel to demonstrate the effectiveness of our workflow.ConclusionsOur workflow contributes to obtaining intact synaptic structures at the sub-nanometer scale through serial section ET, which contains rapid ROI locating, automatic alignment, volume reconstruction, and semi-automatic synapse reconstruction. We have open-sourced the relevant code in our workflow, so it is easy to apply it to other labs and obtain complete 3D ultrastructures which size is similar to intact synapses with sub-nanometer voxel size.

Block belief propagation algorithm for two-dimensional tensor networks

Block belief propagation algorithm for two-dimensional tensor networks

High Throughput and Hardware Efficient Hybrid LDPC Decoder Using Bit-Serial Stochastic Updating

Hybrid low-density parity-check (LDPC) decoding combines conventional Belief-Propagation (BP) algorithm with stochastic decoding to achieve high performance and low complexity simultaneously. However, lossy and inefficient stochastic-to-binary (S2B) conversion brings extra performance degradation and decoding latency. In this paper, a bit-serial stochastic updating based hybrid decoding (BSSU-HD) is proposed, which employs fully correlated stochastic (FCS) check nodes (CNs) and probability tracers assisted variable nodes (VNs) to accomplish accurate and efficient S2B conversion. Two strategies, including random source selection and tracing speed switching, are proposed to further improve performance and convergence. A BSSU LDPC decoder for IEEE 802.3an is designed in a 65-nm CMOS process, which occupies 4.6 mm <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^2$</tex-math> </inline-formula> silicon area and achieves a throughput of 200.8 Gb/s at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E_b/N_0 = 4.4$</tex-math> </inline-formula> dB with 500 MHz clock frequency from a 1.2 V supply voltage. The power and energy efficiency are 2.933 W and 14.61 pJ/bit, respectively. To the best of our known, it achieves the best decoding performance, the highest throughput and hardware efficiency among state-of-the-art IEEE 802.3an LDPC decoders. We also verify that the BSSU-HD can achieve better performance for multi-rate 5th generation (5G) New Ratio (NR) LDPC codes than conventional algorithm, which greatly extends the application of the stochastic decoding.

Distribution Network Topology Identification Using Smart Meter Data and Considering the Same-Bus-Different-Feeder Condition

Due to the rapid growth of distribution systems in urban areas, the increasing complexity of these distribution systems brings challenges to accurate topology identification. The collected voltage data from smart meters have been proven effective in topology identification applications. However, when multiple feeders are connected to the same bus, the accuracy of existing voltage-correlation-based topology identification can be degraded significantly. To address this challenge, a comprehensive inference method is proposed in this paper to identify the on/off switch state in the distribution system considering the same-bus-different-feeder condition. The voltage-power-dependence principle among connected nodes is revealed. Based on this theory, a physical-probabilistic-network (PPN) model is proposed to represent the causal relationships between the switch states and the voltage-power dependence in a distribution network. The belief propagation algorithm is introduced to deduce the topology identification model, which can reduce the time consumption of the inference. The performance of the proposed method and its advantage over the existing methods are verified in case studies.

BP-algorithm based on factor diagram about massive MIMO system

In order to meet the growing demand for high-speed mobile data business, there has been a constant concern for the fifth-generation mobile communication system. 5G large-scale Multiple Input Multiple Output (MIMO) technique has significantly improved the system spectral efficiency and energy efficiency. In order to study the signal detection method under the large-scale MIMO system and improve the existing methods, the article describes the background of signal detection. It introduces the development of the belief propagation (BP) algorithm. There are four main BP algorithms: Original-BP algorithm, RDF-BP algorithm, EBRDF-BP algorithm, and GAI-BP algorithm. One algorithm is proposed based on these fundamental algorithms to improve the whole detection performance. This algorithm reduces complexity while not increasing the error rate too much, which means that it has certain feasibility and practicability.