Marco Pretti - Politecnico di Torino #
Lowering the error floor of Gallager codes: A statistical-mechanical 
view #
 The problem of error correction for Gallager's low-density parity-check 
codes is notoriously equivalent to that of computing marginal Boltzmann 
probabilities for an Ising-like 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 mean-field 
(Bethe-Peierls) approximation. Belief propagation (BP) and similar 
iterative algorithms are an efficient way to perform the calculation, 
but they sometimes fail to converge, giving rise to a nonnegligible 
residual error probability (error floor). On the other hand, 
provably-convergent algorithms are far too complex to be implemented in 
a real decoder. In this work we consider the application of the 
probability damping (PD)* technique, which can be regarded either as a 
variant of BP, of which it retains the low complexity, or as an 
approximation of a provably-convergent algorithm, from which it is 
expected to inherit better convergence properties. We investigate the 
algorithm behavior on a real instance of Gallager code, and compare the 
results with state-of-the-art algorithms.
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* Please note that such an acronym was coined well before the foundation 
of the italian Partito Democratico.