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Dynamic Check message Majority-Logic Decoding Algorithm for Non-binary LDPC Codes

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2014年第6期E97A卷 1356-1364页

作者： Lu, Yichao Peng, Xiao Tian, Guifen Goto, Satoshi Waseda Univ Grad Sch IPS Kitakyushu Fukuoka 8080135 Japan NEC Corp Ltd Kawasaki Kanagawa 2128520 Japan CSRD Toshiba Kawasaki Kanagawa 2118666 Japan

Majority-logic algorithms are devised for decoding non-binary LDPC codes in order to reduce computational complexity. However, compared with conventional belief propagation algorithms, majority-logic algorithms suffer from severe bit error performance degradation. This paper presents a low-complexity reliability-based algorithm aiming at improving error correcting ability of majority-logic algorithms. Reliability measures for check nodes are novelly introduced to realize mutual update between variable message and check message, and hence more efficient reliability propagation can be achieved, similar to belief-propagation algorithm. Simulation results on NB-LDPC codes with different characteristics demonstrate that our algorithm can reduce the bit error ratio by more than one order of magnitude and the coding gain enhancement over ISRB-MLGD can reach 0.2-2.0 dB, compared with both the ISRB-MLGD and IISRB-MLGD algorithms. Moreover, simulations on typical LDPC codes show that the computational complexity of the proposed algorithm is closely equivalent to ISRB-MLGD algorithm, and is less than 10% of Min-max algorithm. As a result, the proposed algorithm achieves a more efficient trade-off between decoding computational complexity and error performance.

关键词： non-binary LDPC codes majority-logic decoding iterative decoding message-passing algorithms

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Minimal dominating set problem studied by simulated annealing and cavity method: analytics and population dynamics

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2017年第10期2017卷 103402-1-103402-24页

作者： Habibulla, Yusupjan Xinjiang Univ Sch Phys & Technol Sheng Li Rd 666 Urumqi 830046 Peoples R China

The minimal dominating set (MDS) problem is a prototypical hard combinatorial optimization problem. We recently studied this problem using the cavity method. Although we obtained a solution for a given graph that gives a very good estimation of the minimal dominating size, we do not know whether there is a ground state solution or how many solutions exist in the ground state. We have therefore continued to develop a one-step replica symmetry breaking theory to investigate the ground state energy of the MDS problem. First, we find that the solution space for the MDS problem exhibits both condensation transition and cluster transition on regular random graphs, and prove this using a simulated annealing dynamical process. Second, we develop a zero-temperature survey propagation algorithm on Erdos-Renyi random graphs to estimate the ground state energy, and obtain a survey propagation decimation algorithm that achieves results as good as the belief propagation decimation algorithm.

关键词： cavity and replica method message-passing algorithms random graphs networks spin glasses

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Correlation enhanced modularity-based belief propagation method for community detection in networks

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2016年第5期2016卷 053301-053301页

作者： Lai, Darong Shu, Xin Nardini, Christine Southeast Univ Sch Comp Sci & Engn Nanjing Jiangsu Peoples R China Southeast Univ Key Lab Comp Network & Informat Integrat Minist Educ Nanjing Jiangsu Peoples R China Nanjing Agr Univ Coll Informat Sci & Technol Nanjing Jiangsu Peoples R China Personalgenomics Str Le Grazie 15 I-37134 Verona Italy

Community structure is an important feature of networks, and the correct detection of communities is a fundamental problem in network analysis. Statistical inference has recently been proposed for successful detection, provided the number of communities can be appropriately estimated a priori. In the absence of such information, model selection by determination of the number of communities remains an issue. We show here that correlation between communities from a highly parceled partition can be used to estimate a narrow range of variation for the real number of communities. This range, further elaborated by modularity-based belief propagation, correctly identifies communities. Testing on synthetic networks generated by a stochastic block model and a set of real-world networks shows that our method can alleviate the effects of modularity fluctuations well and enhance the ability of community detection of the bare modularity-based belief propagation method.

关键词： analysis of algorithms clustering techniques message-passing algorithms random graphs networks

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Sparse Code Multiple Access: Potentials and Challenges

IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY

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IEEE OPEN JOURNAL OF THE COMMUNICATIONS SOCIETY 2021年 2卷 1205-1238页

作者： Rebhi, Manel Hassan, Kais Raoof, Kosai Charge, Pascal Le Mans Univ Lab Acoust Univ Mans F-72085 Le Mans France Univ Nantes Ecole Polytech IETR F-44300 Nantes France

The massive connectivity is among other unprecedented requirements which are expected to be satisfied in order to follow the perpetual increase of connected devices in the era of Internet of Things. In contrast to the family of conventional orthogonal multiple access schemes, the key distinguishing feature of non-orthogonal multiple access (NOMA) is its capacity to support the massive connectivity. Sparse code multiple access (SCMA) is one of the powerful schemes of code-domain NOMA (CD-NOMA) and is among the promising candidates of multiple access techniques to be employed in future generations of wireless communication systems thanks to the sparsity pattern of its codebooks. This technique has been actively investigated in recent years. In this paper, we provide a comprehensive survey of the state-of-the-art of SCMA. First, we will pinpoint SCMA place in the NOMA landscape including power-domain NOMA and CD-NOMA with the aim of justifying why SCMA is prominent. Then, its system architecture is highlighted and its basic principles are presented, afterwards a review of exiting codebook designs and available SCMA detectors is provided, before showing how resources are expected to be assigned, and how SCMA can be combined with other existing and emerging technologies. Finally, we present a range of future research trends and challenging open issues that should be addressed to optimize SCMA performance.

关键词： Wireless communication NOMA Systems architecture Prototypes Detectors Market research Resource management SCMA NOMA code-domain codebook design multi-dimensional constellations message-passing algorithms SCMA detector IoT

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Collaboration in social networks

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2012年第12期109卷 4395-4400页

作者： Dall'Asta, Luca Marsili, Matteo Pin, Paolo Politecn Torino Dipartimento Fis I-10129 Turin Italy Abdus Salam Int Ctr Theoret Phys I-34014 Trieste Italy Coll Carlo Alberto I-10024 Turin Italy Univ Siena Dipartimento Econ Polit I-53100 Siena Italy

The very notion of social network implies that linked individuals interact repeatedly with each other. This notion allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria-that we call "collaborative equilibria"-that have a precise interpretation in terms of subgraphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures where as when incentives exceed a threshold they acquire a nonlocal nature, which requires a "critical mass" of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks.

关键词： constraint-satisfaction problems message-passing algorithms prisoner's dilemma social networks

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Optimal deployment of resources for maximizing impact in spreading processes

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2017年第39期114卷 E8138-E8146页

作者： Lokhov, Andrey Y. Saad, David Los Alamos Natl Lab Ctr Nonlinear Studies & Theoret Div T 4 Los Alamos NM 87545 USA Aston Univ Nonlinear & Complex Res Grp Birmingham B4 7ET W Midlands England

The effective use of limited resources for controlling spreading processes on networks is of prime significance in diverse contexts, ranging from the identification of "influential spreaders" for maximizing information dissemination and targeted interventions in regulatory networks, to the development of mitigation policies for infectious diseases and financial contagion in economic systems. Solutions for these optimization tasks that are based purely on topological arguments are not fully satisfactory;in realistic settings, the problem is often characterized by heterogeneous interactions and requires interventions in a dynamic fashion over a finite time window via a restricted set of controllable nodes. The optimal distribution of available resources hence results from an interplay between network topology and spreading dynamics. We show how these problems can be addressed as particular instances of a universal analytical framework based on a scalable dynamic message-passing approach and demonstrate the efficacy of the method on a variety of real-world examples.

关键词： optimal control of spreading processes dynamic resource allocation message-passing algorithms influence maximization mitigation of epidemic outbreak

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Blind calibration for compressed sensing: state evolution and an online algorithm

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2020年第33期53卷 334004-334004页

作者： Gabrie, Marylou Barbier, Jean Krzakala, Florent Zdeborova, Lenka Univ Paris Sorbonne Univ CNRS Lab PhysEcole Normale SuperENSUniv PSL F-75005 Paris France Abdus Salaam Int Ctr Theoret Phys Trieste Italy Univ Paris Saclay CNRS CEA Inst Phys Theor Paris France

Compressed sensing allows for the acquisition of compressible signals with a small number of measurements. In experimental settings, the sensing process corresponding to the hardware implementation is not always perfectly known and may require a calibration. To this end, blind calibration proposes to perform at the same time the calibrationandthe compressed sensing. Schulke and collaborators suggested an approach based on approximate message passing for blind calibration (cal-AMP) in (Schulke Cet al2013Advances in Neural Information Processing Systems261-9 and Schulke Cet al2015J. Stat. Mech.P11013). Here, their algorithm is extended from the already proposed offline case to the online case, for which the calibration is refined step by step as new measured samples are received. We show that the performance of both the offline and the online algorithms can be theoretically studied via the state evolution formalism. Finally, the efficiency of cal-AMP and the consistency of the theoretical predictions are confirmed through numerical simulations.

关键词： message-passing algorithms statistical inference compressed sensing online learning

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Reliability-based schedule for bit-flipping decoding of low-density parity-check codes

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IEEE TRANSACTIONS ON COMMUNICATIONS 2004年第12期52卷 2038-2040页

作者： Nouh, A Banihashemi, AH Carleton Univ Broadband Communicat & Wireless Syst Ctr Dept Syst & Comp Engn Ottawa ON K1N 6N5 Canada

A reliability-based message-passing schedule for iterative decoding of low-density parity-check codes is proposed. Simulation results for bit-flipping algorithms (with binary messages) show that a reliability-based schedule can provide considerable improvement in performance and decoding speed over the so-called flooding (parallel) schedule, as well as the existing graph-based schedules. The cost associated with this improvement is negligible and is equivalent to having a two-bit representation for initial messages, instead of the standard one bit for hard-decision algorithms, only at the first iteration (all the exchanged messages are still binary).

关键词： bit-flipping (BF) algorithms hard-decision algorithms iterative decoding low-density parity-check (LDPC) codes message-passing algorithms message-passing schedule reliability-based schedule (RBS) schedules for iterative decoding

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Scalable detection of statistically significant communities and hierarchies, using message passing for modularity

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PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA 2014年第51期111卷 18144-18149页

作者： Zhang, Pan Moore, Cristopher Santa Fe Inst Santa Fe NM 87501 USA

Modularity is a popular measure of community structure. However, maximizing the modularity can lead to many competing partitions, with almost the same modularity, that are poorly correlated with each other. It can also produce illusory "communities" in random graphs where none exist. We address this problem by using the modularity as a Hamiltonian at finite temperature and using an efficient belief propagation algorithm to obtain the consensus of many partitions with high modularity, rather than looking for a single partition that maximizes it. We show analytically and numerically that the proposed algorithm works all of the way down to the detectability transition in networks generated by the stochastic block model. It also performs well on real-world networks, revealing large communities in some networks where previous work has claimed no communities exist. Finally we show that by applying our algorithm recursively, subdividing communities until no statistically significant subcommunities can be found, we can detect hierarchical structure in real-world networks more efficiently than previous methods.

关键词： networks community detection message-passing algorithms statistical significance phase transitions

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Semi-analytic approximate stability selection for correlated data in generalized linear models

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JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2020年第9期2020卷

作者： Takahashi, Takashi Kabashima, Yoshiyuki Tokyo Inst Technol Dept Math & Comp Sci Meguro Ku 2-12-1 Ookayama Tokyo Japan Univ Tokyo Inst Phys Intelligence Bunkyo Ku 7-3-1 Hongo Tokyo 1130033 Japan Univ Tokyo Dept Phys Grad Sch Sci Bunkyo Ku 7-3-1 Hongo Tokyo 1130033 Japan

We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is computationally demanding because it needs to fit GLMs to many re-sampled datasets. We propose a novel approximate inference algorithm that can conduct SS without the repeated fitting. The algorithm is based on the replica method of statistical mechanics and vector approximate message passing of information theory. For datasets characterized by rotation-invariant matrix ensembles, we derive state evolution equations that macroscopically describe the dynamics of the proposed algorithm. We also show that their fixed points are consistent with the replica symmetric solution obtained by the replica method. Numerical experiments indicate that the algorithm exhibits fast convergence and high approximation accuracy for both synthetic and real-world data.

关键词： Cavity and replica method message-passing algorithms Statistical inference

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