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Abstract: A belief-propagation decoder for low-density lattice codes is given whichrepresents messages explicitly as a mixture of Gaussians functions. The keycomponent is an algorithm for approximating a mixture of several Gaussians withanother mixture with a smaller number of Gaussians. This Gaussian mixturereduction algorithm iteratively reduces the number of Gaussians by minimizingthe distance between the original mixture and an approximation with one fewerGaussians.Error rates and noise thresholds of this decoder are compared with those forthe previously-proposed decoder which discretely quantizes the messages. Theerror rates are indistinguishable for dimension 1000 and 10000 lattices, andthe Gaussian-mixture decoder has a 0.2 dB loss for dimension 100 lattices. TheGaussian-mixture decoder has a loss of about 0.03 dB in the noise threshold,which is evaluated via Monte Carlo density evolution. Further, theGaussian-mixture decoder uses far less storage for the messages.



Author: Brian M. Kurkoski, Justin Dauwels

Source: https://arxiv.org/



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