Complementary Graph Entropy, AND Product, and Disjoint Union of Graphs

In the zero-error Slepian-Wolf source coding problem, the optimal rate is given by the complementary graph entropy $\overline{H}$ of the characteristic graph. It has no single-letter formula, except for perfect graphs, for the pentagon graph with uniform distribution $G_5$, and for their disjoint union. We consider two particular instances, where the characteristic graphs respectively write as an AND product $\wedge$, and as a disjoint union $\sqcup$. We derive a structural result that equates $\overline{H}(\wedge \: \cdot)$ and $\overline{H}(\sqcup \: \cdot)$ up to a multiplicative constant, which has two consequences. First, we prove that the cases where $\overline{H}(\wedge \:\cdot)$ and $\overline{H}(\sqcup \: \cdot)$ can be linearized coincide. Second, we determine $\overline{H}$ in cases where it was unknown: products of perfect graphs; and $G_5 \wedge G$ when $G$ is a perfect graph, using Tuncel et al.'s result for $\overline{H}(G_5 \sqcup G)$. The graphs in these cases are not perfect in general

Machine Learning in Digital Signal Processing for Optical Transmission Systems

The future demand for digital information will exceed the capabilities of current optical communication systems, which are approaching their limits due to component and fiber intrinsic non-linear effects. Machine learning methods are promising to find new ways of leverage the available resources and to explore new solutions. Although, some of the machine learning methods such as adaptive non-linear filtering and probabilistic modeling are not novel in the field of telecommunication, enhanced powerful architecture designs together with increasing computing power make it possible to tackle more complex problems today. The methods presented in this work apply machine learning on optical communication systems with two main contributions. First, an unsupervised learning algorithm with embedded additive white Gaussian noise (AWGN) channel and appropriate power constraint is trained end-to-end, learning a geometric constellation shape for lowest bit-error rates over amplified and unamplified links. Second, supervised machine learning methods, especially deep neural networks with and without internal cyclical connections, are investigated to combat linear and non-linear inter-symbol interference (ISI) as well as colored noise effects introduced by the components and the fiber. On high-bandwidth coherent optical transmission setups their performances and complexities are experimentally evaluated and benchmarked against conventional digital signal processing (DSP) approaches. This thesis shows how machine learning can be applied to optical communication systems. In particular, it is demonstrated that machine learning is a viable designing and DSP tool to increase the capabilities of optical communication systems

Colour local feature fusion for image matching and recognition

This thesis investigates the use of colour information for local image feature extraction. The work is motivated by the inherent limitation of the most widely used state of the art local feature techniques, caused by their disregard of colour information. Colour contains important information that improves the description of the world around us, and by disregarding it; chromatic edges may be lost and thus decrease the level of saliency and distinctiveness of the resulting grayscale image. This thesis addresses the question of whether colour can improve the distinctive and descriptive capabilities of local features, and if this leads to better performances in image feature matching and object recognition applications. To ensure that the developed local colour features are robust to general imaging conditions and capable for real-world applications, this work utilises the most prominent photometric colour invariant gradients from the literature. The research addresses several limitations of previous studies that used colour invariants, by implementing robust local colour features in the form of a Harris-Laplace interest region detection and a SIFT description which characterises the detected image region. Additionally, a comprehensive and rigorous evaluation is performed, that compares the largest number of colour invariants of any previous study. This research provides for the first time, conclusive findings on the capability of the chosen colour invariants for practical real-world computer vision tasks. The last major aspect of the research involves the proposal of a feature fusion extraction strategy, that uses grayscale intensity and colour information conjointly. Two separate fusion approaches are implemented and evaluated, one for local feature matching tasks and another approach for object recognition. Results from the fusion analysis strongly indicate, that the colour invariants contain unique and useful information that can enhance the performance of techniques that use grayscale only based features