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Lattice codes can achieve capacity on the AWGN channel

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2 Author(s)
Urbanke, R. ; Bell Labs., Murray Hill, NJ, USA ; Rimoldi, B.

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)

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Information Theory, IEEE Transactions on  (Volume:44 ,  Issue: 1 )