The modulo loss in lattice dirty-paper coding

Ram Zamir*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Lattice decoding of a lattice-shaped codebook is a simple alternative for ML decoding, and it is equivalent to ML decoding after modulo-lattice reduction of the channel output. For good (high-dimensional) lattices, this modulo operation is information lossless in the presence of AWGN. At a finite shaping dimension, however, the lattice decoder is inferior to direct ML decoding from the channel output. The 'modulo loss' is particularly large at low SNR, and it gets up to 4dB for scalar shaping. We consider the effect of a known interference (i.e., a dirty-paper channel) on the gap between the two decoders. We show that in the limit of a strong interference, the modulo output becomes a sufficient statistic for decoding the input. Thus, in the strong-interference regime, ML decoding suffers the same 'modulo loss' as lattice decoding.

Original languageEnglish
Title of host publication2014 IEEE International Symposium on Information Theory, ISIT 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages4
ISBN (Print)9781479951864
StatePublished - 2014
Event2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States
Duration: 29 Jun 20144 Jul 2014

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Conference2014 IEEE International Symposium on Information Theory, ISIT 2014
Country/TerritoryUnited States
CityHonolulu, HI


  • ML decoding
  • dirty-paper coding
  • known interference
  • lattice encoding and decoding
  • modulo-lattice
  • structured binning
  • sufficient statistics


Dive into the research topics of 'The modulo loss in lattice dirty-paper coding'. Together they form a unique fingerprint.

Cite this