scholarly journals Analysis of TDMP Algorithm of LDPC Codes Based on Density Evolution and Gaussian Approximation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 457 ◽  
Author(s):  
Xiumin Wang ◽  
Hong Chang ◽  
Jun Li ◽  
Weilin Cao ◽  
Liang Shan
Keyword(s):  
Message Passing ◽  
Belief Propagation ◽  
Gaussian Approximation ◽  
Bp Algorithm ◽  
Turbo Decoding ◽  
Density Evolution ◽  
Analysis Process ◽  
Evolution Analysis ◽  
Simplified Algorithm ◽  
Previous Iteration

Based on density evolution analysis of the existing belief propagation (BP) algorithm, the Turbo Decoding Message Passing (TDMP) algorithm was analyzed from the perspective of density evolution and Gaussian approximation, and the theoretical analysis process of TDMP algorithm was given. When calculating the prior message of each layer of the TDMP algorithm, the check message of the previous iteration should be subtracted. Therefore, the result will not be convergent, if the TDMP algorithm is directly analyzed based on density evolution and Gaussian approximation. We researched the TDMP algorithm based on the symmetry conditions to obtain the convergent result. When using density evolution (DE) and Gaussian approximation to analyze the decoding convergence of the TDMP algorithm, we can provide a theoretical basis for proving the superiority of the algorithm. Then, based on the DE theory, we calculated the probability density function (PDF) of the check-to-variable information of TDMP and its simplified algorithm, and then gave it a calculation based on the process of the normalization factor. Simulation results show that the decoding convergence speed of the TDMP algorithm was faster and the iterations were smaller compared to the BP algorithm under the same conditions.

scholarly journals New explicitly invertible approximation of the function involved in LDPC codes density evolution analysis using a Gaussian approximation

2019 ◽  
Vol 55 (22) ◽  
pp. 1183-1186 ◽  
Author(s):  
F. Vatta ◽  
A. Soranzo ◽  
M. Comisso ◽  
G. Buttazzoni ◽  
F. Babich
Keyword(s):  
Gaussian Approximation ◽  
Ldpc Codes ◽  
Density Evolution ◽  
Evolution Analysis

scholarly journals Recovering a hidden community beyond the Kesten–Stigum threshold in O(|E|log*|V|) time

2018 ◽  
Vol 55 (2) ◽  
pp. 325-352 ◽  
Author(s):  
Bruce Hajek ◽  
Yihong Wu ◽  
Jiaming Xu
Keyword(s):  
Message Passing ◽  
Belief Propagation ◽  
Linear Time ◽  
Signal To Noise Ratio ◽  
Bp Algorithm ◽  
Local Algorithm ◽  
Message Passing Algorithm ◽  
Edge Probability ◽  
Effective Signal ◽  
Total Time Complexity

Abstract Community detection is considered for a stochastic block model graph of n vertices, with K vertices in the planted community, edge probability p for pairs of vertices both in the community, and edge probability q for other pairs of vertices. The main focus of the paper is on weak recovery of the community based on the graph G, with o(K) misclassified vertices on average, in the sublinear regime n1-o(1) ≤ K ≤ o(n). A critical parameter is the effective signal-to-noise ratio λ = K2(p - q)2 / ((n - K)q), with λ = 1 corresponding to the Kesten–Stigum threshold. We show that a belief propagation (BP) algorithm achieves weak recovery if λ > 1 / e, beyond the Kesten–Stigum threshold by a factor of 1 / e. The BP algorithm only needs to run for log*n + O(1) iterations, with the total time complexity O(|E|log*n), where log*n is the iterated logarithm of n. Conversely, if λ ≤ 1 / e, no local algorithm can asymptotically outperform trivial random guessing. Furthermore, a linear message-passing algorithm that corresponds to applying a power iteration to the nonbacktracking matrix of the graph is shown to attain weak recovery if and only if λ > 1. In addition, the BP algorithm can be combined with a linear-time voting procedure to achieve the information limit of exact recovery (correctly classify all vertices with high probability) for all K ≥ (n / logn) (ρBP + o(1)), where ρBP is a function of p / q.

scholarly journals Quaternary Message Passing Decoding of LDPC Codes: Density Evolution Analysis and Error Floor

2021 ◽  
Author(s):  
Emna Ben Yacoub ◽  
Balazs Matuz ◽  
Alexandre Graell i Amat ◽  
Gianluigi Liva
Keyword(s):  
Message Passing ◽  
Ldpc Codes ◽  
Error Floor ◽  
Density Evolution ◽  
Evolution Analysis

scholarly journals Cooperative Localization for Mobile Networks: A Distributed Belief Propagation–Mean Field Message Passing Algorithm

2016 ◽  
Vol 23 (6) ◽  
pp. 828-832 ◽  
Author(s):  
Burak Cakmak ◽  
Daniel N. Urup ◽  
Florian Meyer ◽  
Troels Pedersen ◽  
Bernard H. Fleury ◽  
...  
Keyword(s):  
Mobile Networks ◽  
Message Passing ◽  
Belief Propagation ◽  
Mean Field ◽  
Cooperative Localization ◽  
Message Passing Algorithm

scholarly journals Constraint Satisfaction by Survey Propagation

2005 ◽  
Author(s):  
Alfredo Braunstein ◽  
Marc Mézard
Keyword(s):  
Constraint Satisfaction ◽  
Message Passing ◽  
Statistical Physics ◽  
Belief Propagation ◽  
Solution Space ◽  
Error Correcting Codes ◽  
Constraint Satisfaction Problems ◽  
Probabilistic Methods ◽  
Survey Propagation ◽  
Algorithmic Strategy

Methods and analyses from statistical physics are of use not only in studying the performance of algorithms, but also in developing efficient algorithms. Here, we consider survey propagation (SP), a new approach for solving typical instances of random constraint satisfaction problems. SP has proven successful in solving random k-satisfiability (k -SAT) and random graph q-coloring (q-COL) in the “hard SAT” region of parameter space [79, 395, 397, 412], relatively close to the SAT/UNSAT phase transition discussed in the previous chapter. In this chapter we discuss the SP equations, and suggest a theoretical framework for the method [429] that applies to a wide class of discrete constraint satisfaction problems. We propose a way of deriving the equations that sheds light on the capabilities of the algorithm, and illustrates the differences with other well-known iterative probabilistic methods. Our approach takes into account the clustered structure of the solution space described in chapter 3, and involves adding an additional “joker” value that variables can be assigned. Within clusters, a variable can be frozen to some value, meaning that the variable always takes the same value for all solutions (satisfying assignments) within the cluster. Alternatively, it can be unfrozen, meaning that it fluctuates from solution to solution within the cluster. As we will discuss, the SP equations manage to describe the fluctuations by assigning joker values to unfrozen variables. The overall algorithmic strategy is iterative and decomposable in two elementary steps. The first step is to evaluate the marginal probabilities of frozen variables using the SP message-passing procedure. The second step, or decimation step, is to use this information to fix the values of some variables and simplify the problem. The notion of message passing will be illustrated throughout the chapter by comparing it with a simpler procedure known as belief propagation (mentioned in ch. 3 in the context of error correcting codes) in which no assumptions are made about the structure of the solution space. The chapter is organized as follows. In section 2 we provide the general formalism, defining constraint satisfaction problems as well as the key concepts of factor graphs and cavities, using the concrete examples of satisfiability and graph coloring.

Efficient nonparametric belief propagation for pose estimation and manipulation of articulated objects

2019 ◽  
Vol 4 (30) ◽  
pp. eaaw4523 ◽  
Author(s):  
Karthik Desingh ◽  
Shiyang Lu ◽  
Anthony Opipari ◽  
Odest Chadwicke Jenkins
Keyword(s):  
Pose Estimation ◽  
Message Passing ◽  
Belief Propagation ◽  
Sensor Data ◽  
Depth Sensor ◽  
Continuous Space ◽  
Articulated Objects ◽  
Message Passing Algorithm ◽  
Wide Range ◽  
Object Part

Robots working in human environments often encounter a wide range of articulated objects, such as tools, cabinets, and other jointed objects. Such articulated objects can take an infinite number of possible poses, as a point in a potentially high-dimensional continuous space. A robot must perceive this continuous pose to manipulate the object to a desired pose. This problem of perception and manipulation of articulated objects remains a challenge due to its high dimensionality and multimodal uncertainty. Here, we describe a factored approach to estimate the poses of articulated objects using an efficient approach to nonparametric belief propagation. We consider inputs as geometrical models with articulation constraints and observed RGBD (red, green, blue, and depth) sensor data. The described framework produces object-part pose beliefs iteratively. The problem is formulated as a pairwise Markov random field (MRF), where each hidden node (continuous pose variable) is an observed object-part’s pose and the edges denote the articulation constraints between the parts. We describe articulated pose estimation by a “pull” message passing algorithm for nonparametric belief propagation (PMPNBP) and evaluate its convergence properties over scenes with articulated objects. Robot experiments are provided to demonstrate the necessity of maintaining beliefs to perform goal-driven manipulation tasks.

Research of the Multi-State Deteriorating System Failure Based on RPN and the Multi-Granularity Linguistic System

2013 ◽  
Vol 443 ◽  
pp. 594-598 ◽  
Author(s):  
Yan Li ◽  
Zi Li Zhang ◽  
Hong Li Yuan
Keyword(s):  
Iteration Algorithm ◽  
System Failure ◽  
New Approach ◽  
Analysis Process ◽  
Evolution Analysis ◽  
Linguistic System ◽  
Deteriorating Process ◽  
Optimal Maintenance ◽  
Policy Iteration Algorithm ◽  
Fault Evolution

Traditional FMEA lacks systematicness. A new approach of multi-state deteriorating system failure assessment is proposed base on the risk priority number (RPN) and multi-granularity linguistic information system. With this method, the key links and parameters of system deteriorating process is clear, and fault evolution analysis is more comprehensive. Policy iteration algorithm is introduced to calculate the optimal maintenance strategy under different fault conditions. Finally, numerical examples illustrate the failure analysis process; the results show that the new approach is efficient and practical.

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