Encoding and Decoding Construction D' Lattices for Power-Constrained Communications

This paper focuses on the encoding and decoding of Construction D' coding lattices that can be used with shaping lattices for power-constrained channels. Two encoding methods and a decoding algorithm for Construction D' lattices are given. A design of quasi-cyclic low-density parity-check (QC-LDPC) codes to form Construction D' lattices is presented. This allows construction of nested lattice codes which are good for coding, good for shaping, and have low-complexity encoding and decoding. Numerical results using
$E_{8},\ BW_{16}$
and Leech lattices for shaping a Construction D' lattice indicate that the shaping gains 0.65 dB, 0.86 dB and 1.03 dB are preserved, respectively.