Instanton-based techniques for analysis and reduction of error floor of LDPC codes

Journal Article · Tue Jan 01 04:00:00 EST 2008 · IEEE Journal on Selected Areas in Communications

OSTI ID:960924

Chertkov, Michael ^[1]; Chilappagari, Shashi K ^[1]; Stepanov, Mikhail G ^[1]; Vasic, Bane ^[2]

---

1. Los Alamos National Laboratory
2. SENIOR MEMBER, IEEE

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.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: DOE
• DOE Contract Number: AC52-06NA25396
• OSTI ID: 960924
• Report Number(s): LA-UR-08-06553; LA-UR-08-6553
• Journal Information: IEEE Journal on Selected Areas in Communications, Journal Name: IEEE Journal on Selected Areas in Communications Journal Issue: 6 Vol. 27; ISSN 0733-8716
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ERRORS
FAILURES
INSTANTONS
LINEAR PROGRAMMING
NOISE
OPTIMIZATION
REDUCTION