Bounds on maximum likelihood decoding performance for linear codes at low rates

Hideki Yagi, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


For a given linear code (ensemble), upper bounds on the error probability under maximum likelihood decoding are investigated at low rates. A class of symmetric memoryless channels suitable for Bhattacharyya-type bounds, which are particularly of importance at low rates, is introduced. Over a symmetric channel, a lower bound on the error exponent is derived for a given linear code. A sufficient condition for achieving the expurgated exponent, which is the best among known error exponents at low rates, within a fixed discrepancy is given. Over a general discrete memoryless channel, the same analysis provides a lower bound on the average error exponent for an ensemble of coset codes generated by a given linear code. The bounding technique is extended to the case of generalized maximum likelihood decoding with erasure and list-decoding options.

Original languageEnglish (US)
Article number6478823
Pages (from-to)4482-4497
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2013

All Science Journal Classification (ASJC) codes

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


  • Error exponent
  • Expurgated exponent
  • Low-rate region
  • Maximum likelihood (ML) decoding
  • Structured codes


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