"Random Network Coding and Designs over Finite Fields"
Hey everybody,
I enclose here something that I think is very cool and could be a source of inspiration for current research on other topics. Please *do* cite them if you use them as a source of inspiration. These are one of the best primers around on Random Network Coding and Designs over Finite Fields.
You'll find my dissertation and slides (+ overview work on a similar topic) that I co-authored during my master thesis in 2013. I hold a double MS in Telecommunications from UAB and UPC (+ Chartered Engineer in the EUROPEAN Union).
Title: Construction and Performance of Network Codes.
Description:
The main goal of this work is to implement and provide a theoretical description for different schemes of Physical-layer Network Coding. Using a basic scheme as starting point, the project presents the construction and performance of different systems of communications with increasing complexity. The project is structured in different parts: first, an introduction to Physical-layer Network Coding and Lattice Network Codes is done. Next, the mathematical tools needed to understand the system of Compute and Forward (C&F) are presented. Further, the 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 coefficient A are studied and implemented.
This thesis was developed as a joint work with I. de Zarzà i Cubero at the Department of Mathematics. Here is her corresponding thesis:
Title: Physical-layer Network Coding: Design of Constellations over Rings.
Description:
The main goal of this work is to design constellations in a system of Physical-layer Network Coding. The design is based on constellations over two commutative rings: GAUSSIAN Integers and EISENSTEIN Integers. Using this particular system as a working base, first we have identified the needed theory in the design, as well as the needed performance metrics in order to analyse the proposed constellations. Then, we have presented the most used constellations nowadays in order to be used as a comparison. Finally, we have proposed a design methodology and four constellations. Further, the obtained results have been analysed and the particular studied system of Physical-layer Network Coding has been implemented.
