Expander graph arguments for message-passing algorithms

D. Burshtein*, G. Miller

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We show how expander-based arguments may be used to prove that message-passing algorithms can correct a linear number of erroneous messages. The implication of this result is that when the block length is sufficiently large, once a message-passing algorithm has corrected a sufficiently large fraction of the errors, it will eventually correct all errors. This result is then combined with known results on the ability of message-passing algorithms to reduce the number of errors to an arbitrarily small fraction for relatively high transmission rates. The results hold for various message-passing algorithms, inchiding Gallager's hard-decision and soft-decision (with clipping) decoding algorithms. Our results assume low-density parity-check (LDPC) codes based on an irregular bipartite graph.

Original languageEnglish
Pages (from-to)782-790
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - Feb 2001


  • Belief propagation
  • Expander graph
  • Iterative decoding
  • Low-density parity-check (LDPC) codes


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