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Lowering the error floor of Gallager codes: a statisticalmechanical viewThe problem of error correction for Gallager's lowdensity paritycheck codes is notoriously equivalent to that of computing marginal Boltzmann probabilities for an Isinglike model with multispin interactions in a nonuniform magnetic field. Since the graph of interactions is locally a tree, the solution is very well approximated by a generalized meanfield (BethePeierls) approximation. Belief propagation (BP) and similar iterative algorithms are an efficient way to perform the calculation, but they sometimes fail to converge, or converge to noncodewords, giving rise to a nonnegligible residual error probability (error floor). On the other hand, provablyconvergent algorithms are far too complex to be implemented in a real decoder. In this work we consider the application of the probabilitydamping technique, which can be regarded either as a variant of BP, from which it retains the property of low complexity, or as an approximation of a provablyconvergent algorithm, from which it is expected to inherit better convergence properties. We investigate the algorithm behaviour on a real instance of Gallager code, and compare the results with stateoftheart algorithms. Date:
Thu, 18/12/2014  14:30
Speaker:
Marco Pretti (Politecnico Torino)
Place:
Sala Affrescata, HuGeF, Molecular Biology Center (MBC), Via Nizza 52
