Lattices which are good for (almost) everything

Uri Erez*, Simon Litsyn, Ram Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We define an ensemble of lattices, and show that for asymptotically high dimension most of its members are simultaneously good as sphere packings, sphere coverings, additive white Gaussian noise (AWGN) channel codes and mean-squared error (MSE) quantization codes. These lattices are generated by applying Construction A to a random linear code over a prime field of growing size, i.e., by "lifting" the code to ℝn.

Original languageEnglish
Pages (from-to)3401-3416
Number of pages16
JournalIEEE Transactions on Information Theory
Issue number10
StatePublished - Oct 2005


  • Coding for unconstrained additive white Gaussian noise (AWGN) channel
  • Lattice codes
  • Loeliger ensemble
  • Meansquared error (MSE) quantization
  • Minkowski bound
  • Poltyrev exponent
  • Sphere covering
  • Sphere packing

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