  Two encoding methods and a decoding algorithm for Construction D' coding
lattices that can be used with shaping lattices for power-constrained channels
are given. We construct nested lattice codes which are good for coding, good
for shaping, and have low-complexity encoding and decoding. An indexing method
for nested lattice codes is modified to avoid an integer overflow problem at
high dimension. Convolutional code generator polynomials for Construction A
lattices with the greatest shaping gain are given, the result of an extensive
search. It is shown that rate 1/3 convolutional codes provide a more favorable
performance-complexity trade-off than rate 1/2 convolutional codes. For a given
dimension, tail-biting convolutional codes have higher shaping gain than that
of zero-tailed convolutional codes. A design for quasi-cyclic low-density
parity-check (LDPC) codes to form Construction D' lattices is presented, where
their parity-check matrices can be easily triangularized, thus enabling
efficient encoding and indexing. The resulting LDPC Construction D' lattices
are evaluated using four shaping lattices: the $E_8$ lattice, the $BW_{16}$
lattice, the Leech lattice and our best-found convolutional code lattice,
showing a shaping gain of approximately 0.65 dB, 0.86 dB, 1.03 dB and 1.25 dB
at dimension 2304.
