Stopping set distribution of LDPC code ensembles

Alon Orlitsky, Krishnamurthy Viswanathan, Junan Zhang

Research output: Contribution to journalArticlepeer-review

157 Scopus citations


Stopping sets determine the performance of low-density parity-check (LDPC) codes under iterative decoding over erasure channels. We derive several results on the asymptotic behavior of stopping sets in Tanner-graph ensembles, including the following. An expression for the normalized average stopping set distribution, yielding, in particular, a critical fraction of the block length above which codes have exponentially many stopping sets of that size. A relation between the degree distribution and the likely size of the smallest nonempty stopping set, showing that for a √1 - λ′ (0)ρp′(1) fraction of codes with λ′(0)ρ ′(1) < 1, and in particular for almost all codes with smallest variable degree > 2, the smallest nonempty stopping set is linear in the block length. Bounds on the average block error probability as a function of the erasure probability ε, showing in particular that for codes with lowest variable degree 2, if ε is below a certain threshold, the asymptotic average block error probability is 1 - √1 - λ′(0)ρp′(1)ε.

Original languageEnglish (US)
Pages (from-to)929-953
Number of pages25
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - Mar 2005
Externally publishedYes


  • Binary erasure channel (BEC)
  • Block error probability
  • Growth rate
  • Low-density parity-check (LDPC) codes
  • Minimum distance
  • Stopping set

ASJC Scopus subject areas

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


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