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...
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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.
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 give...
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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.
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...
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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.
We analyse the local stability of the high-temperature fixed point of the loopy belief propagation (LBP) algorithm and how this relates to the properties of the Bethe free energy which LBP tries to minimize. We focus ...
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We analyse the local stability of the high-temperature fixed point of the loopy belief propagation (LBP) algorithm and how this relates to the properties of the Bethe free energy which LBP tries to minimize. We focus on the case of binary networks with pairwise interactions. In particular, we state sufficient conditions for convergence of LBP to a unique fixed point and show that these are sharp for purely ferromagnetic interactions. In contrast, in the purely antiferromagnetic case, the undamped parallel LBP algorithm is suboptimal in the sense that the stability of the fixed point breaks down much earlier than for damped or sequential LBP;we observe that the onset of instability for the latter algorithms is related to the properties of the Bethe free energy. For spinglass interactions, damping LBP only helps slightly. We estimate analytically the temperature at which the high-temperature LBP fixed point becomes unstable for random graphs with arbitrary degree distributions and random interactions.
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...
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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.
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...
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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.
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 ...
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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.
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 perfe...
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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 messagepassing 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.
This paper discusses inference problems in probabilistic graphical models that often occur in a machine learning setting. In particular it presents a unified view of several recently proposed approximation schemes. Ex...
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This paper discusses inference problems in probabilistic graphical models that often occur in a machine learning setting. In particular it presents a unified view of several recently proposed approximation schemes. Expectation consistent approximations and expectation propagation are both shown to be related to Bethe free energies with weak consistency constraints, i.e. free energies where local approximations are only required to agree on certain statistics instead of full marginals.
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 sc...
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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).
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