Lattice codes can achieve capacity on the AWGN channel

  • Authors:
  • R. Urbanke;B. Rimoldi

  • Affiliations:
  • Bell Labs., Murray Hill, NJ;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

It is shown that lattice codes can achieve capacity on the additive white Gaussian noise channel. More precisely, for any rate R less than capacity and e>0, there exists a lattice code with rate no less than R and average error probability upper-bounded by e. These lattice codes include all points of the (translated) lattice within the spherical bounding region (not just the ones inside a thin spherical shell)