TY - JOUR
T1 - Instanton-based techniques for analysis and reduction of error floors of LDPC codes
AU - Chilappagari, Shashi Kiran
AU - Chertkov, Michael
AU - Stepanov, Mikhail G.
AU - Vasic, Bane
N1 - Funding Information:
Part of the work by S. K. Chilappagari was performed when he was a summer GRA at LANL. The work at LANL, by S. K. Chilappagari and M. Chertkov, was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396. B. Va-sic and S. K. Chilappagari would like to acknowledge the financial support of the NSF (Grants CCF-0634969 and IHCS-0725405) and Seagate Technology. M. G. Stepanov would like to acknowledge the support of NSF grant DMS-0807592. The authors would like to thank A. R. Krishnan for providing the modified code and the anonymous reviewers for their suggestions.
PY - 2009/8
Y1 - 2009/8
N2 - We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result in decoding failures. We show that the general idea and the respective optimization technique are applicable broadly to a variety of channels, discrete or continuous, and variety of sub-optimal decoders. Specifically, we consider: iterative belief propagation (BP) decoders, Gallager type decoders, and linear programming (LP) decoders performing over the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC). The instanton analysis suggests that the underlying topological structures of the most probable instanton of the same code but different channels and decoders are related to each other. Armed with this understanding of the graphical structure of the instanton and its relation to the decoding failures, we suggest a method to construct codes whose Tanner graphs are free of these structures, and thus have less significant error floors.
AB - We describe a family of instanton-based optimization methods developed recently for the analysis of the error floors of low-density parity-check (LDPC) codes. Instantons are the most probable configurations of the channel noise which result in decoding failures. We show that the general idea and the respective optimization technique are applicable broadly to a variety of channels, discrete or continuous, and variety of sub-optimal decoders. Specifically, we consider: iterative belief propagation (BP) decoders, Gallager type decoders, and linear programming (LP) decoders performing over the additive white Gaussian noise channel (AWGNC) and the binary symmetric channel (BSC). The instanton analysis suggests that the underlying topological structures of the most probable instanton of the same code but different channels and decoders are related to each other. Armed with this understanding of the graphical structure of the instanton and its relation to the decoding failures, we suggest a method to construct codes whose Tanner graphs are free of these structures, and thus have less significant error floors.
KW - Error Floor
KW - Instantons
KW - Iterative Decoding
KW - Linear Programming Decoding
KW - Low-density parity-check codes
KW - Pseudo-Codewords
KW - Trapping Sets
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U2 - 10.1109/JSAC.2009.090804
DO - 10.1109/JSAC.2009.090804
M3 - Article
AN - SCOPUS:84055222321
VL - 27
SP - 855
EP - 865
JO - IEEE Journal on Selected Areas in Communications
JF - IEEE Journal on Selected Areas in Communications
SN - 0733-8716
IS - 6
M1 - 5174515
ER -