This paper describes the implementation of network coding on OpenGL-enabled graphics cards. Network coding is an interesting approach to increase the capacity and robustness in multi-hop networks. The current problem is to implement random linear network coding on mobile devices which are limited in computational power, energy, and memory. Some mobile devices are equipped with a 3D graphics accelerator, which could be used to do most of the RLNC related calculations. Such a cross-over have already been used in com putationally demanding research tasks as in physics or medicine. As a first step the paper focuses on the implementation of RLNC using the OpenGL library and NVidia's Cg toolkit on desktop PCs and laptops. Several measurement results show that the implementation on the graphics accelerator is outperforming the CPU by a significant margin. The OpenGL implementation performs relatively better with larger generation sizes due to the parallel nature of GPUs. Therefore the paper shows an appealing solution for the future to perform network coding on mobile devices.

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A number of people have supported me during the work which has culminated into this dissertation. First and foremost, I would like to thank my main supervisor Arne Lakså. His deep enthusiasm for the field of research, sharing of knowledge in many aspects, support and guidance during the period of the project have been invaluable. My co-supervisor, Knut Mørken, has taken care of many practical and organizational arrangements at the UiO. He has provided constructive feedback which was very useful in order to compile a final version of this text.Then I would like to thank Børre Bang for his patience in discussions of theoretical and practical matters, sharing of his ideas and for always taking the time to provide constructive feedback and advice. Lubomir Dechevsky has prepared the ground by initiating and developing the theory of expo-rational B-splines and other topics. He has provided valuable feedback at several occasions. Klas Pettersson has been supportive through providing his expertise in mathematical theory and analysis, and by coordinating a series of interesting seminars on the topic of differential geometry. Peter Zanaty has put his mark by performing efficient and thorough work, which undoubtedly has influenced the way I work.My dear friend and colleague Jostein Bratlie has spent what seems like an uncountable number of hours together with me. Together we have been learning, researching, programming, writing, traveling and teaching, just to mention a few, throughout the period of the research project.My friends and colleagues at Narvik University College are always positive and provide a great working atmosphere. They are an interesting group of people with knowledge in many fields. The open door policy is much appreciated. This thesis would not have been realized without the funding from the Verdikt program (project id 201511) by the Research Council of Norway.I would like to thank my friends and family for the understanding and patience during long working hours. My parents, Randi and Magne, and my parents in law, Solveig and Ole, have taken care of my family while I have been away traveling to attend research conferences. My daughters, Evine and Alvilde, have been dragging me out of "deep hack mode" to remind me of the most important aspects of life.Last, but not least, a big warm hug to my wife and best friend Therese for showing patience and for putting up with me during this period. v

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