Bounds on the maximum-likelihood decoding error probability of low-density parity-check codes

Gadi Miller*, David Burshtein

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent.

Original languageEnglish
Pages (from-to)2696-2710
Number of pages15
JournalIEEE Transactions on Information Theory
Volume47
Issue number7
DOIs
StatePublished - Nov 2001

Keywords

  • Code ensembles
  • Error exponent
  • Low-density parity-check (LDPC) codes

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