This work describes a method of approximating matrix permanents efficiently using belief propagation. We formulate a probability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this partition function. After deriving some speedups to standard belief propagation, the resulting algorithm requires O(n) time per iteration and seems empirical...

—Loopy belief propagation (BP) is an effective solution for assigning labels to the nodes of a graphical model such as the Markov random field (MRF), but it requires high memory, bandwidth, and computational costs. Furthermore, the iterative, pixel-wise, and sequential operations of BP make it difficult to parallelize the computation. In this paper, we propose two techniques to address these is...

Two new iterative soft decision decoding methods for Reed-Solomon (RS) codes are proposed. These methods are based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In the first propos...

Tracking an unknown number of low-observable objects is notoriously challenging. This letter proposes a sequential Bayesian estimation method based on the track-before-detect (TBD) approach. In TBD, raw sensor measurements are directly used by tracking algorithm without any preprocessing. Our proposed new statistical model that introduces object hypothesis for each data cell measurements. It al...

The paper presents an iterative version of join-tree clustering that applies the message passing of join-tree clustering algorithm to join-graphs rather than to join-trees, iteratively. It is inspired by the success of Pearl’s belief propagation algorithm (BP) as an iterative approximation scheme on one hand, and by a recently introduced mini-clustering (MC(i)) success as an anytime approximati...

We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. The algorithm constructs adaptively efficient proposal distributions approximating the local beliefs at each note of the MRF. This is achieved by considering proposal distributions in the exponential family whose parameters are...

We apply belief propagation (BP) to multi–user detection in a spread spectrum system, under the assumption of Gaussian symbols. We prove that BP is both convergent and allows to estimate the correct conditional expectation of the input symbols. It is therefore an optimal –minimum mean square error– detection algorithm. This suggests the possibility of designing BP detection algorithms for more ...

We consider communication over binary memoryless symmetric channels using random elements from irregular low density parity check code (LDPC) ensembles, and belief propagation (BP) decoding. Under the assumption that the corresponding Tanner graph includes a non-vanishing fraction of degree 2 variable nodes, we determine the large blocklength behavior of the bit error rate for noise levels belo...

Belief propagation (BP) is an increasingly popular method of performing approximate inference on arbitrary graphical models. At times, even further approximations are required, whether from quantization or other simplified message representations or from stochastic approximation methods. Introducing such errors into the BP message computations has the potential to adversely affect the solution ...