Multilevel Lattice Codes From Hurwitz Quaternion Integers
Juliana G. F. Souza, Sueli I. R. Costa, Cong Ling · IEEE Transactions on Information Theory · 2025
This work presents an extension of the Construction πAlattices proposed by Huang and Narayanan, 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 analyse the performance of the resulting multilevel lattice codes and highlight via computer simulations their notably reduced computational complexity provided by the multistage decoding. Moreover, it is shown that there is a sequence of Construction πAlattices that attain with high probability the Poltyrev-limit.