An LDPCC decoding algorithm based on Bowman-Levin approximation --Comparison with BP and CCCP--

Belief propagation (BP) and the concave convex procedure (CCCP) are both methods that utilize the Bethe free energy as a cost function and solve information processing tasks. We have developed a new algorithm that also uses the Bethe free energy, but changes the roles of the master variables and the slave variables. This is called the Bowman-Levin (BL) approximation in the domain of statistical physics. When we applied the BL algorithm to decode the Gallager ensemble of short-length regular low-density parity check codes (LDPCC) over an additive white Gaussian noise (AWGN) channel, its average performance was somewhat better than that of either BP or CCCP. This implies that the BL algorithm can also be successfully applied to other problems to which BP or CCCP has already been applied.Comment: 2005 IEEE International Symposium on Information Theor

Communication Network Design: Balancing Modularity and Mixing via Optimal Graph Spectra

By leveraging information technologies, organizations now have the ability to design their communication networks and crowdsourcing platforms to pursue various performance goals, but existing research on network design does not account for the specific features of social networks, such as the notion of teams. We fill this gap by demonstrating how desirable aspects of organizational structure can be mapped parsimoniously onto the spectrum of the graph Laplacian allowing the specification of structural objectives and build on recent advances in non-convex programming to optimize them. This design framework is general, but we focus here on the problem of creating graphs that balance high modularity and low mixing time, and show how "liaisons" rather than brokers maximize this objective

Distributed Reconstruction of Nonlinear Networks: An ADMM Approach

In this paper, we present a distributed algorithm for the reconstruction of large-scale nonlinear networks. In particular, we focus on the identification from time-series data of the nonlinear functional forms and associated parameters of large-scale nonlinear networks. Recently, a nonlinear network reconstruction problem was formulated as a nonconvex optimisation problem based on the combination of a marginal likelihood maximisation procedure with sparsity inducing priors. Using a convex-concave procedure (CCCP), an iterative reweighted lasso algorithm was derived to solve the initial nonconvex optimisation problem. By exploiting the structure of the objective function of this reweighted lasso algorithm, a distributed algorithm can be designed. To this end, we apply the alternating direction method of multipliers (ADMM) to decompose the original problem into several subproblems. To illustrate the effectiveness of the proposed methods, we use our approach to identify a network of interconnected Kuramoto oscillators with different network sizes (500~100,000 nodes).Comment: To appear in the Preprints of 19th IFAC World Congress 201