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It is now well established that iterative decoding approaches the performance of Maximum Likelihood Decoding of sparse graph codes, asymptotically in the block length. For a finite length sparse code, iterative decoding fails on specific subgraphs generically termed as trapping sets. Trapping sets give rise to error floor, an abrupt degradation of the code error performance in the high signal to noise...
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al., which allows to use the same objective function (Kullback-Leibler divergence) as a starting point. In this method message passing fixed point equations (which correspond to the update rules...
Applying the max-product (and belief-propagation) algorithms to loopy graphs is now quite popular for constraint satisfaction problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there is no general understanding of the conditions required for convergence and/or the optimality of converged solutions. This paper presents an analysis of weighted...
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