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Geometry on the parameter space of the belief propagation algorithm on Bayesian networks

PHYSICS LETTERS A 2006年第1-2期350卷 81-86页

作者： Watanabe, Y Res Org Informat & Syst Natl Inst Informat Chiyoda Ku Tokyo 1018430 Japan RIKEN Brain Sci Inst Lab Math Neurosci Wako Saitama 3510198 Japan

This Letter considers a geometrical structure on the parameter space of the belief propagation algorithm on Bayesian networks. The statistical manifold of posterior distributions is introduced, and the expression for the information metric on the manifold is derived. The expression is used to construct a cost function which can be regarded as a measure of the distance in the parameter space. (c) 2005 Elsevier B.V. All rights reserved.

关键词： statistical manifold belief propagation algorithm Bayesian networks

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On the convergence of loopy belief propagation algorithm for different update rules

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2006年第2期E89A卷 575-582页

作者： Taga, N Mase, S Tokyo Inst Technol Tokyo 1528552 Japan

The belief propagation (BP) algorithm is a tool with which one can calculate beliefs, marginal probabilities, of probabilistic networks without loops (e.g., Bayesian networks) in a time proportional to the number of nodes. For networks with loops, it may not converge and, even if it converges, beliefs may not be equal to exact marginal probabilities although its application is known to give remarkably good results such as in the coding theory. Tatikonda and Jordan show a theoretical result on the convergence of the algorithm for probabilistic networks with loops in terms of the theory of Markov random fields on trees and give a sufficient condition of the convergence of the algorithm. In this paper, we discuss the "impatient" update rule as well as the "lazy" update rule discussed in Tatikonda and Jordan. In the viewpoint of the theory of Markov random fields, it is shown that the rule for updating both gives essentially the same results and the impatient update rule is expected to converge faster than the lazy one. Numerical experiments are also given.

关键词： belief propagation algorithm Markov random field unwrapped network phase transition

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Serially concatenated scheme of polar codes and the improved belief propagation decoding algorithm

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IET COMMUNICATIONS 2020年第14期14卷 2309-2318页

作者： Mao, Yinyou Yang, Dong Liu, Xingcheng Xie, Yi Sun Yat Sen Univ Sch Elect & Informat Technol Guangzhou Peoples R China Sun Yat Sen Univ Xinhua Coll Sch Informat Sci Guangzhou Peoples R China Sun Yat Sen Univ Sch Data & Comp Sci Guangzhou Peoples R China

In this study, a serially concatenated scheme of polar codes with convolutional codes is proposed to improve the error correction performance. The novel belief propagation (BP) decoding algorithm addresses two issues that are present in the currently available BP decoding algorithms. The first issue is the poor performance of the BP decoding algorithms, in particular the introduction of an error floor. The second is the component codes can only use systematic codes in the traditional concatenated scheme of polar codes with convolutional codes, which inhibits the effective update of the prior information of the redundant check bits. The proposed BP decoding algorithm is based on right-directed message processing, which effectively improves the decoding performance. In addition, the proposed concatenated scheme extends the selection of component codes from the systematic polar codes to the non-systematic polar codes. Hence, the areas of applications and the prior information of information bits for polar codes are expanded and more effectively updated, respectively. The simulation results show that the proposed scheme is much better than the traditional concatenated scheme, and the error floor is no longer introduced in terms of the block error rate, while the storage and computational complexities have not increased obviously.

关键词： convolutional codes computational complexity iterative decoding concatenated codes polar codes belief propagation concatenation codes belief propagation algorithm component codes convolutional codes decoding performance systematic polar codes nonsystematic polar codes serially concatenated scheme novel BP decoding algorithm

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A Recommendation algorithm Based on belief propagation and Probability Matrix Factorization 18

A Recommendation Algorithm Based on Belief Propagation and P...

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18th IEEE International Conference on Pervasive Intelligent and Computing (PICom)

作者： Li, Juan Wang, Xiao-Feng Feng, Wan-Jing North Minzu Univ Dept Comp Sci & Engn Yinchuan 750021 Ningxia Peoples R China Ningxia Key Lab Intelligent Informat & Big Data P Yinchuan 750021 Ningxia Peoples R China

ISBN: (纸本)9781728166094

Collaborative filtering recommendation algorithm is the most important recommended application methods at present. The selection of users (items) similarity measurement methods in this method may affect the final recommendation effect. Probability matrix factorization algorithm is one of the more and more methods applied in collaborative filtering algorithms. This paper proposes to convert the users (items) consumption network into a bipartite graph and use belief propagation algorithm to obtain fuzzy nearest neighbor set, improving users (items) similarity measure and incorporating it into probability matrix factorization. Experimental tests on the data set showed that the proposed method performance was good.

关键词： component bipartite graph belief propagation algorithm probability matrix factorization nearest neighbors

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

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IEEE TRANSACTIONS ON COMMUNICATIONS 2002年第3期50卷 406-414页

作者： Chen, JH Fossorier, MPC Univ Hawaii Manoa Dept Elect Engn Honolulu HI 96822 USA

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.

关键词： belief propagation algorithm iterative decoding low-density parity check codes

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Node Selection for belief propagation Based Channel Equalization

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IEICE TRANSACTIONS ON COMMUNICATIONS 2017年第8期E100B卷 1285-1292页

作者： Hagiwara, Mitsuyoshi Nishimura, Toshihiko Ohgane, Takeo Ogawa, Yasutaka Hokkaido Univ Grad Sch Informat Sci & Technol Sapporo Hokkaido 0600814 Japan

Recently, much progress has been made in the study of belief propagation (BP) based signal detection with large-scale factor graphs. When we apply the BP algorithm to equalization in a SISO multipath channel, the corresponding factor graph has many short loops and patterns in an edge connection/strength. Thus, proper convergence may not be achieved. In general, the log-likelihood ratio (LLR) oscillates in ill-converged cases. Therefore, LLR oscillation avoidance is important for BP-based equalization. In this paper, we propose applying node selection (NS) to prevent the LLR from oscillating. The NS extends the loop length virtually by a serial LLR update. Thus, some performance improvement is expected. Simulation results show that the error floor is significantly reduced by NS in the uncoded case and that the NS works very well in the coded case.

关键词： belief propagation algorithm log-likelihood ratio interference canceller equalization

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State Estimation in Electric Power Systems Using belief propagation: An Extended DC Model 17

State Estimation in Electric Power Systems Using Belief Prop...

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17th IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC)

作者： Cosovic, Mirsad Vukobratovic, Dejan Schneider Elect DMS NS LLC Novi Sad Serbia Univ Novi Sad Dept Power Elect & Commun Engn Novi Sad 21000 Serbia

ISBN: (纸本)9781509017492

In this paper, we model an extended DC state estimation (SE) in an electric power system as a factor graph (FG) and solve it using belief propagation (BP) algorithm. The DC model comprises bus voltage angles as state variables, while the extended DC model includes bus voltage angles and bus voltage magnitudes as state variables. By applying BP to solve the SE problem in the extended DC model, we obtain a Gaussian BP scenario for which we derive closed-form expressions for BP messages exchanged along the FG. The performance of the BP algorithm is demonstrated for the IEEE 14 bus test case. Finally, the application of BP algorithm on the extended DC scenario provides significant insights into a fundamental structure of BP equations in more complex models such as the AC model - the topic we will investigate in our follow up work. As a side-goal of this paper, we aim at thorough and detailed presentation on applying BP on the SE problem in order to make the powerful BP algorithm more accessible and applicable within the power-engineering community.

关键词： State Estimation Electric Power System Factor Graph belief propagation algorithm Gaussian belief propagation

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Design and Implementation of a belief propagation Detector for Sparse Channels

Design and Implementation of a Belief Propagation Detector f...

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22nd IEEE International Conference on Application-Specific Systems, Architectures and Processors (ASAP)

作者： Peng, Yanjie Zhang, Kai Klein, Andrew G. Huang, Xinming Worcester Polytech Inst Dept Elect & Comp Engn Worcester MA 01609 USA

ISBN: (纸本)9781457712920

In this paper, we address the design and implementation of the symbol detector for sparse channels which are described as having long spanning durations but sparse multipath structure. The traditional maximum-likelihood (ML) algorithm provides an optimal performance to eliminate the multipath effect, however its complexity scales exponentially with the channel length. As a more efficient symbol detection algorithm through sparse channels, the iterative belief propagation (BP) algorithm has a complexity merely dependent on the number of nonzero channel coefficients, while achieving a near-optimal error performance. We present the architecture design for a reconfigurable low-complexity high-throughput BP detector. As an example, we implement a BP detector for quadrature phase-shift keying (QPSK) modulation on Xilinx Virtex 5 FPGA with a maximum frequency of 252 MHz and equivalently a throughput of 100.8 Mb/s at 5 iterations.

关键词： belief propagation algorithm sparse channel symbol detection architecture design

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A Novel Labeling Scheme for Neural belief propagation in Polar Codes 19

A Novel Labeling Scheme for Neural Belief Propagation in Pol...

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19th IEEE International Wireless Communications and Mobile Computing (IEEE IWCMC)

作者： Chen, Qi Ju, Hao Xu, Yin He, Dazhi Zhang, Wenjun Shanghai Jiao Tong Univ Cooperat Media Network Innovat Ctr CMIC Sch Elect Informat & Elect Engn Shanghai Peoples R China Pengcheng Lab Shenzhen Peoples R China

ISBN: (纸本)9798350333398

Recently, deep learning has been adopted to improve the performance of the belief propagation algorithm in polar codes, namely, the neural belief propagation decoder. By attaching trainable parameters to each edge on a tanner graph, this decoder effectively weakens the effect of short cycles. In this paper, we will show that the decoder can be further improved with our newly-designed labeling scheme. Instead of ground-truth transmitted codewords, our scheme utilizes codewords generated from a high-performance decoder (i.e., noise-aided belief propagation list decoder) to construct loss functions. Besides, to reduce the labeling complexity, the ground-truth transmitted codewords are integrated into the decoder as a list and compared with the other lists with the principle of minimum Euclidean distance. Numerical simulation results demonstrate that the proposed labeling scheme can improve the decoding performance by up to 0.2 dB with the same run time complexity and model size.

关键词： Polar codes deep learning belief propagation algorithm

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Single mode Quasi-cyclic LDPC Decoder Using Modified belief propagation 3

Single mode Quasi-cyclic LDPC Decoder Using Modified Belief ...

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3rd International Conference on Communications and Signal Processing (ICCSP)

作者： Mankar, Monica V. Patil, Abha Asutkar, G. M. Rashtrasant Tukadoji Maharaj Nagpur Univ Dept Elect Engn Yeshwantrao Chavan Coll Engn Nagpur Maharashtra India Rashtrasant Tukadoji Maharaj Nagpur Univ Dept Elect & Commun Engn Priyadarshini Inst Engn & Technol Nagpur Maharashtra India

ISBN: (纸本)9781479933587

Low Density Parity Check codes (LDPC) have shown good error correcting performance which enables efficient and reliable communication. A subclass of LDPC codes known as quasi-cyclic LDPC codes are used whose parity check matrices consists of circulant permutation matrices. QC-LDPC codes require less memory as compared to LDPC codes. This paper presents a low complexity quasi-cyclic low density parity check (QC-LDPC) decoder. QC-LDPC codes require less memory as compared to LDPC codes. Partially parallel, low complexity decoder architecture has been designed for single-mode decoding. This decoder is modeled in Verilog, synthesized and performed place and route for the design using Xilinx ISE 12.1.

关键词： belief propagation algorithm LDPC codes QC-LDPC Single mode decoder

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