The random coding bound is tight for the average linear code or lattice

Yuval Domb, Ram Zamir, Meir Feder

Research output: Contribution to journalArticlepeer-review


In 1973, Gallager proved that the random-coding bound is exponentially tight for the random code ensemble at all rates, even below expurgation. This result explained that the random-coding exponent does not achieve the expurgation exponent due to the properties of the random ensemble, irrespective of the utilized bounding technique. It has been conjectured that this same behavior holds true for a random ensemble of linear codes. This conjecture is proved in this paper. In addition, it is shown that this property extends to Poltyrev's random-coding exponent for a random ensemble of lattices.

Original languageEnglish
Article number7312995
Pages (from-to)121-130
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - 1 Jan 2016


  • Code ensembles
  • Error exponent
  • Lattices
  • Linear codes
  • Lower bounding techniques
  • Random-coding


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