TY - GEN

T1 - Loop calculus helps to improve belief propagation and linear programming decodings of low-density-parity-check codes

AU - Chertkov, Michael

AU - Chernyak, Vladimir Y.

PY - 2006

Y1 - 2006

N2 - We illustrate the utility of the recently developed loop calculus [1], [2] 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 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.

AB - We illustrate the utility of the recently developed loop calculus [1], [2] 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 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.

UR - http://www.scopus.com/inward/record.url?scp=84940656304&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84940656304

T3 - 44th Annual Allerton Conference on Communication, Control, and Computing 2006

SP - 31

EP - 40

BT - 44th Annual Allerton Conference on Communication, Control, and Computing 2006

PB - University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering

T2 - 44th Annual Allerton Conference on Communication, Control, and Computing 2006

Y2 - 27 September 2006 through 29 September 2006

ER -