Construction and Performance of Network Codes

The main goal of this work is to implement and provide a theoretical description of different schemes of Physical-layer Network Coding. Using a basic setup as starting point, the manuscript presents the construction and performance of different systems of communications with increasing complexity. The text is structured in different sections: first, an introduction to Physical-layer Network Coding and Lattice Network Codes is delivered. Next, the mathematical tools required to understand the system of Compute and Forward (C&F) are presented. Further, a first basic scheme is analysed and implemented. The next step consists on implementing a vectorial C&F System and a HAMMING q-ary coded version. Finally, different approaches to improve the matrix of coefficients are studied and implemented.<div><p style="text-align: justify;">The main goal of this work is to implement and provide a theoretical description of different schemes of Physical-layer Network Coding. Using a basic setup as starting point, the manuscript presents the construction and performance of different systems of communications with increasing complexity.</p><p style="text-align: justify;"> </p><p style="text-align: justify;">The text is structured in different sections: first, an introduction to Physical-layer Network Coding and Lattice Network Codes is delivered. Next, the mathematical tools required to understand the system of Compute and Forward (C&F) are presented. Further, a first basic scheme is analysed and implemented. The next step consists on implementing a vectorial C&F System and a HAMMING q-ary coded version. Finally, different approaches to improve the matrix of coefficients are studied and implemented.</p></div>