Construction $\pi_{A}$ Lattices Extended to Hurwitz Quaternion Integers

In this work we extend the Construction
$\pi_{A}$
lattices proposed in [1], to Hurwitz quaternion integers. This construction is provided by using an isomorphism from a version of the Chinese remainder theorem applied to maximal orders in contrast to natural orders in prior works. Exploiting this map, we analyze the performance of the resulting multilevel lattice codes and show via computer simulations their notably reduced computational complexity provided by the multistage decoding.