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

Shashi Kiran Chilappagari, Michael Chertkov, Mikhail G. Stepanov, Bane Vasic

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


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.

Original languageEnglish (US)
Article number5174515
Pages (from-to)855-865
Number of pages11
JournalIEEE Journal on Selected Areas in Communications
Issue number6
StatePublished - Aug 2009


  • Error Floor
  • Instantons
  • Iterative Decoding
  • Linear Programming Decoding
  • Low-density parity-check codes
  • Pseudo-Codewords
  • Trapping Sets

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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