Pseudocodewords of tanner graphs

Christine A. Kelley, Deepak Sridhara

Research output: Contribution to journalArticlepeer-review

60 Scopus citations


This paper presents a detailed analysis of pseudocodewords of Tanner graphs. Pseudocodewords arising on the iterative decoder's computation tree are distinguished from pseudocodewords arising on finite degree lifts. Lower bounds on the minimum pseudocodeword weight are presented for the BEC, BSC, and AWGN channel. Some structural properties of pseudocodewords are examined, and pseudocodewords and graph properties that are potentially problematic with min-sum iterative decoding are identified. An upper bound on the minimum degree lift needed to realize a particular irreducible lift-realizable pseudocodeword is given in terms of its maximal component, and it is shown that all irreducible lift-realizable pseudocodewords have components upper bounded by a finite value t that is dependent on the graph structure. Examples and different Tanner graph representations of individual codes are examined and the resulting pseudocodeword distributions and iterative decoding performances are analyzed. The results obtained provide some insights in relating the structure of the Tanner graph to the pseudocodeword distribution and suggest ways of designing Tanner graphs with good minimum pseudocodeword weight.

Original languageEnglish (US)
Pages (from-to)4013-4038
Number of pages26
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - Nov 2007
Externally publishedYes


  • Iterative decoding
  • Low-density parity-check (LDPC) codes
  • Min-sum iterative decoder
  • Pseudocodewords

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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