Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Visual Hand Tracking Using Nonparametric Belief Propagation
CVPRW '04 Proceedings of the 2004 Conference on Computer Vision and Pattern Recognition Workshop (CVPRW'04) Volume 12 - Volume 12
Loopy Belief Propagation: Convergence and Effects of Message Errors
The Journal of Machine Learning Research
Walk-Sums and Belief Propagation in Gaussian Graphical Models
The Journal of Machine Learning Research
Fixing convergence of Gaussian belief propagation
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Single-Gaussian messages and noise thresholds for decoding low-density lattice codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Efficient parametric decoder of low density lattice codes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Bayesian compressive sensing via belief propagation
IEEE Transactions on Signal Processing
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Turbo decoding as an instance of Pearl's “belief propagation” algorithm
IEEE Journal on Selected Areas in Communications
Nonparametric belief propagation for self-localization of sensor networks
IEEE Journal on Selected Areas in Communications
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The recent work of Sommer, Feder and Shalvi presented a new family of codes called low density lattice codes (LDLC) that can be decoded efficiently and approach the capacity of the AWGN channel. A linear time iterative decoding scheme which is based on a message-passing formulation on a factor graph is given. In the current work we report our theoretical findings regarding the relation between the LDLC decoder and belief propagation. We show that the LDLC decoder is an instance of non-parametric belief propagation and further connect it to the Gaussian belief propagation algorithm. Our new results enable borrowing knowledge from the non-parametric and Gaussian belief propagation domains into the LDLC domain. Specifically, we give more general convergence conditions for convergence of the LDLC decoder (under the same assumptions of the original LDLC convergence analysis). We discuss how to extend the LDLC decoder from Latin square to full rank, non-square matrices. We propose an efficient construction of sparse generator matrix and its matching decoder. We report preliminary experimental results which show our decoder has comparable symbol to error rate compared to the original LDLC decoder.