Lattice network coding over finite rings

Lattice network coding is recently proposed as a practical implementation of Nazer-Gastpar's compute-and-forward relaying strategy. Previous investigation of lattice network coding is mainly over finite fields. In this paper, we extend lattice network coding from finite fields to finite rings. In addition to having its own theoretical interest, this extension provides an alternative viewpoint of Nazer-Gastpar's relaying strategy and this extension expands the design space of lattice network codes. In particular, we show that this extension enables the use of complex Construction D to design lattice network codes, leading to potentially higher encoder rates.