In this thesis, Compute-and-Forward is considered, where the system model consists of
multiple users and a single base station. Compute-and-Forward is a type of lattice network
coding which is deemed to avoid backhaul load and is therefore an important aspect
of modern wireless communications networks. Initially we propose an implementation of
construction D into Compute-and-Forward and investigate the implementation of multilayer
lattice encoding and decoding strategies. Here we show that adopting a construction
D lattice we can implement a practical lattice decoder in Compute-and-Forward. During
this investigation and implementation of multilayer lattice encoding and decoding we discover
an error floor due to an interaction between code layers in the multilayer decoder.
We analyse and describe this interaction with mathematical expressions and give detail
using lemmas and proofs. Secondly, we demonstrate the BER performance of the system
model for unit valued channels, integer valued channels and complex integer valued channels.
We show that using the derived expressions for interaction that the decoders on each
code layer are able to indeed decode. The BER results are demonstrated for two scenarios
using zero order and second order Reed-Muller codes and first and third order Reed-Muller
codes. Finally, we extend our system model using construction D and existing conventional
decoders to include coefficient selection algorithms. We employ an exhaustive search algorithm
and analyse the throughput performance of the codes. Again, we extend this to both
our models. With the throughput of the codes we see that each layer can be successfully
decoded considering the interaction expressions. The purpose of the performance results
is to show decodability with the extension of using differing codes
