diff --git a/latex/thesis/chapters/acknowledgements.tex b/latex/thesis/chapters/acknowledgements.tex new file mode 100644 index 0000000..1d2321e --- /dev/null +++ b/latex/thesis/chapters/acknowledgements.tex @@ -0,0 +1,18 @@ +\chapter*{Acknowledgements} + +I would like to thank Prof. Dr.-Ing. Laurent Schmalen for granting me the +opportunity to write my bachelor's thesis at the Communications Engineering Lab, +as well as all other members of the institute for their help and many productive +discussions, and for creating a very pleasant environment to do research in. + +I am very grateful to Dr.-Ing. Holger Jäkel +for kindly providing me with his knowledge and many suggestions, +and for his constructive criticism during the preparation of this work. + +Special thanks also to Mai Anh Vu for her invaluable feedback and support +during the entire undertaking that is this thesis. + +Finally, I would like to thank my family, who have enabled me to pursue my +studies in a field I thoroughly enjoy and who have supported me completely +throughout my journey. + diff --git a/latex/thesis/chapters/introduction.tex b/latex/thesis/chapters/introduction.tex index 3f319fd..2aa2681 100644 --- a/latex/thesis/chapters/introduction.tex +++ b/latex/thesis/chapters/introduction.tex @@ -27,12 +27,13 @@ of the \ac{MAP} decoding problem \cite{proximal_paper}. The motivation behind applying optimization methods to channel decoding is to utilize existing techniques in the broad field of optimization theory, as well -as find new decoding methods not suffering from the same disadvantages or exhibiting -other desirable properties. +as find new decoding methods not suffering from the same disadvantages as +existing message passing based approaches, or exhibiting other desirable properties. \Ac{LP} decoding, for example, comes with strong theoretical guarantees -allowing it to be used as a way of closely approximating \ac{ML} decoding, +allowing it to be used as a way of closely approximating \ac{ML} decoding +\cite[Sec. I]{original_admm}, and proximal decoding is applicable to non-trivial channel models such -as \ac{LDPC}-coded massive \ac{MIMO} channels. +as \ac{LDPC}-coded massive \ac{MIMO} channels \cite{proximal_paper}. This thesis aims to further the analysis of optimization based decoding algorithms as well as verify and complement the considerations present in diff --git a/latex/thesis/chapters/theoretical_background.tex b/latex/thesis/chapters/theoretical_background.tex index 4cb0f79..63358eb 100644 --- a/latex/thesis/chapters/theoretical_background.tex +++ b/latex/thesis/chapters/theoretical_background.tex @@ -179,9 +179,9 @@ codewords: &= \argmax_{c\in\mathcal{C}} \frac{f_{\boldsymbol{Y} \mid \boldsymbol{C}} \left( \boldsymbol{y} \mid \boldsymbol{c} \right) p_{\boldsymbol{C}} \left( \boldsymbol{c} \right)}{f_{\boldsymbol{Y}}\left( \boldsymbol{y} \right) } \\ - &= \argmax_{c\in\mathcal{C}} f_{\boldsymbol{Y} \mid \boldsymbol{C}} - \left( \boldsymbol{y} \mid \boldsymbol{c} \right) p_{\boldsymbol{C}} - \left( \boldsymbol{c} \right) \\ +% &= \argmax_{c\in\mathcal{C}} f_{\boldsymbol{Y} \mid \boldsymbol{C}} +% \left( \boldsymbol{y} \mid \boldsymbol{c} \right) p_{\boldsymbol{C}} +% \left( \boldsymbol{c} \right) \\ &= \argmax_{c\in\mathcal{C}}f_{\boldsymbol{Y} \mid \boldsymbol{C}} \left( \boldsymbol{y} \mid \boldsymbol{c} \right) .\end{align*} @@ -342,7 +342,7 @@ In contrast to the established message-passing decoding algorithms, the perspective then changes from observing the decoding process in its Tanner graph representation with \acp{VN} and \acp{CN} (as shown in figure \ref{fig:dec:tanner}) to a spatial representation (figure \ref{fig:dec:spatial}), -where the codewords are some of the edges of a hypercube. +where the codewords are some of the vertices of a hypercube. The goal is to find the point $\tilde{\boldsymbol{c}}$, which minimizes the objective function $g$. diff --git a/latex/thesis/thesis.tex b/latex/thesis/thesis.tex index 439fc64..f2741bd 100644 --- a/latex/thesis/thesis.tex +++ b/latex/thesis/thesis.tex @@ -35,7 +35,7 @@ \usetikzlibrary{spy} \usetikzlibrary{shapes.geometric} \usetikzlibrary{arrows.meta,arrows} -\tikzset{>=stealth} +\tikzset{>=latex} \pgfplotsset{compat=newest} \usepgfplotslibrary{colorbrewer} @@ -210,6 +210,7 @@ % % 6. Conclusion + \include{chapters/acknowledgements} \tableofcontents \cleardoublepage % make sure multipage TOCs are numbered correctly