Improving convergence of Belief Propagation decoding

M. G. Stepanov; M. Chertkov

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arXiv · cs/0607112

Improving convergence of Belief Propagation decoding

M. G. Stepanov·M. Chertkov

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Abstract

The decoding of Low-Density Parity-Check codes by the Belief Propagation (BP) algorithm is revisited. We check the iterative algorithm for its convergence to a codeword (termination), we run Monte Carlo simulations to find the probability distribution function of the termination time, n_it. Tested on an example [155, 64, 20] code, this termination curve shows a maximum and an extended algebraic tail at the highest values of n_it. Aiming to reduce the tail of the termination curve we consider a family of iterative algorithms modifying the standard BP by means of a simple relaxation. The relaxation parameter controls the convergence of the modified BP algorithm to a minimum of the Bethe free energy. The improvement is experimentally demonstrated for Additive-White-Gaussian-Noise channel in some range of the signal-to-noise ratios. We also discuss the trade-off between the relaxation parameter of the improved iterative scheme and the number of iterations.

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M. G. Stepanov, M. Chertkov. 2006-07-25. Improving convergence of Belief Propagation decoding. https://arxiv.org/abs/cs/0607112

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