On error exponents of modulo lattice additive noise channels

Tie Liu, Pierre Moulin, Ralf Koetter

Research output: Contribution to journalArticlepeer-review


Modulo lattice additive noise (MLAN) channels appear in the analysis of structured binning codes for Costa's dirty-paper channel and of nested lattice codes for the additive white Gaussian noise (AWGN) channel. In this paper, we derive a new lower bound on the error exponents of the MLAN channel. With a proper choice of the shaping lattice and the scaling parameter, the new lower bound coincides with the random-coding lower bound on the error exponents of the AWGN channel at the same signal-to-noise ratio (SNR) in the sphere-packing and straight-line regions. This result implies that, at least for rates close to channel capacity, 1) writing on dirty paper is as reliable as writing on clean paper; and 2) lattice encoding and decoding suffer no loss of error exponents relative to the optimal codes (with maximum-likelihood decoding) for the AWGN channel.

Original languageEnglish (US)
Pages (from-to)454-471
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - Feb 2006


  • Additive white Gaussian noise (AWGN) channel
  • Costa's dirty-paper channel
  • Error exponents
  • Lattice decoding
  • Modulo lattice additive noise (MLAN) channel
  • Nested lattice codes

ASJC Scopus subject areas

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


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