Minor wording changes

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.
+

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
+as find new decoding methods not suffering from the same disadvantages as
-other desirable properties.
+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

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}}
+%    &= \argmax_{c\in\mathcal{C}} f_{\boldsymbol{Y} \mid \boldsymbol{C}}
-        \left( \boldsymbol{y} \mid \boldsymbol{c} \right) p_{\boldsymbol{C}}
+%        \left( \boldsymbol{y} \mid \boldsymbol{c} \right) p_{\boldsymbol{C}}
-        \left( \boldsymbol{c} \right) \\
+%        \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 $g$.
 

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