LATTICE CODES CAN ACHIEVE CAPACITY ON THE AWGN CHANNEL

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