Multilevel lattice codes from Hurwitz quaternion integers

TL;DR

This paper extends multilevel lattice codes to Hurwitz quaternion integers using a Chinese remainder theorem approach, demonstrating improved decoding efficiency and capacity achievement through theoretical analysis and simulations.

Contribution

It introduces a novel construction of lattice codes from Hurwitz quaternion integers using an isomorphism and Chinese remainder theorem, enhancing decoding efficiency and capacity performance.

Findings

Reduced computational complexity in decoding

Effective attainment of the Poltyrev-limit

Performance validated by computer simulations

Abstract

This work presents an extension of the Construction $\pi_A$ lattices proposed in \cite{huang2017construction}, 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, highlight via computer simulations their notably reduced computational complexity provided by the multistage decoding. Moreover it is shown that this construction effectively attain the Poltyrev-limit.