Loop Calculus Helps to Improve Belief Propagation and Linear Programming Decodings of Low-Density-Parity-Check Codes

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dc.creatorChertkov, Michael
dc.creatorChernyak, Vladimir Y.
dc.date2006-09-28
dc.date.accessioned2026-07-07T08:16:43Z
dc.date.available2026-07-07T08:16:43Z
dc.descriptionWe illustrate the utility of the recently developed loop calculus for improving the Belief Propagation (BP) algorithm. If the algorithm that minimizes the Bethe free energy fails we modify the free energy by accounting for a critical loop in a graphical representation of the code. The log-likelihood specific critical loop is found by means of the loop calculus. The general method is tested using an example of the Linear Programming (LP) decoding, that can be viewed as a special limit of the BP decoding. Considering the (155,64,20) code that performs over Additive-White-Gaussian-Noise channel we show that the loop calculus improves the LP decoding and corrects all previously found dangerous configurations of log-likelihoods related to pseudo-codewords with low effective distance, thus reducing the code's error-floor.
dc.description10 pages, 2 figures; Invited talk at 44-th annual Allerton Conference on Communications, Control and Computing, Sep 27-Sep 29, 2006
dc.identifierhttps://arxiv.org/abs/cs/0609154
dc.identifierhttp://arxiv.org/abs/cs/0609154
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133881
dc.subjectInformation Theory
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.titleLoop Calculus Helps to Improve Belief Propagation and Linear Programming Decodings of Low-Density-Parity-Check Codes
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