Power-constrained communications using LDLC lattices

An explicit code construction for using low-density lattice codes (LDLC) on the constrained power AWGN channel is given. LDLC lattices can be decoded in high dimension, so that the code relies on the Euclidean distance between codepoints. A sublattice of the coding lattice is used for code shaping. Lattice codes are designed using the continuous approximation, which allows separating the contribution of the shaping region and coding lattice to the total transmit power. Shaping and lattice decoding are both performed using a belief-propagation decoding algorithm. At a rate of 3 bits per dimension, a dimension 100 code which is 3.6 dB from the sphere bound is found.