Computer Science – Information Theory
Scientific paper
2006-09-28
Computer Science
Information Theory
10 pages, 2 figures; Invited talk at 44-th annual Allerton Conference on Communications, Control and Computing, Sep 27-Sep 29,
Scientific paper
We 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.
Chernyak Vladimir Y.
Chertkov Michael
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