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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
10 pages, 2 figures; Invited talk at 44-th annual Allerton Conference on Communications, Control and Computing, Sep 27-Sep 29, 2006

Keywords

Information Theory, Disordered Systems and Neural Networks, Statistical Mechanics

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/133881

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cs/0609154
 http://arxiv.org/abs/cs/0609154

Collections

arXiv