Rewrote introduction

latex/thesis/chapters/introduction.tex

@@ -6,26 +6,38 @@ of data by detecting and correcting any errors that may occur during
 its transmission or storage.
 One class of binary linear codes, \ac{LDPC} codes, has become especially
 popular due to being able to reach arbitrarily small probabilities of error
-at code rates up to the capacity of the channel, while retaining a structure
+at code rates up to the capacity of the channel \cite[Sec. II.B.]{mackay_rediscovery},
-that allows for very efficient decoding.
+while retaining a structure that allows for very efficient decoding.
 While the established decoders for \ac{LDPC} codes, such as \ac{BP} and the
 \textit{min-sum algorithm}, offer reasonable decoding performance, they are suboptimal
 in most cases and exhibit an \textit{error floor} for high \acp{SNR},
-making them unsuitable for applications with extreme reliability requiremnts.
+making them unsuitable for applications with extreme reliability requirements.
 Optimization based decoding algorithms are an entirely different way of approaching
-the decoding problem, in some cases coming with stronger theoretical guarantees
+the decoding problem.
-and promising to alleviate the error floor issue \cite[Sec. I]{original_admm}.
+The initial introduction of optimization techniques as a way of decoding binary
+linear codes was conducted in Feldman's 2003 Ph.D. thesis and subsequent paper,
+establishing the field of \ac{LP} decoding \cite{feldman_thesis}, \cite{feldman_paper}.
+There, the \ac{ML} decoding problem is approximated by a \textit{linear program},
+a linear, convex optimization problem, which can subsequently be solved using
+a number of different algorithms \cite{alp}, \cite{interior_point},
+\cite{original_admm}, \cite{pdd}.
+More recently, novel approaches such as \textit{proximal decoding} have been
+introduced. Proximal decoding is based on a non-convex optimization formulation
+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.
+\Ac{LP} decoding, for example, comes with strong theoretical guarantees
+allowing it to be used as a way of closely approximating \ac{ML} decoding,
+and proximal decoding is applicable to non-trivial channel models such
+as \ac{LDPC}-coded massive \ac{MIMO} channels.
 
 This thesis aims to further the analysis of optimization based decoding
-algorithms as well as verify and generalize the considerations present in
+algorithms as well as verify and complement the considerations present in
-the existing literature by considering a variety of different codes.
+the existing literature.
-Specifically, the \textit{proximal decoding} \cite{proximal_paper}
+Specifically, the proximal decoding algorithm and \ac{LP} decoding using
-algorithm and \ac{LP} decoding using the \ac{ADMM} \cite{original_admm} are explored.
+the \ac{ADMM} \cite{original_admm} are explored within the context of
-The two algorithms are analyzed based on their theoretical structure
+\ac{BPSK} modulated \ac{AWGN} channels.
-and based on the results of the simulations conducted in the scope of this work.
-Approaches to determine the optimal value of each parameter are derived
-and the computational and decoding performance of the algorithms is examined.
-An improvement on proximal decoding is suggested, achieving up to $\SI{1}{dB}$
-of gain, depending on the parameters chosen and the
-code considered.
 

latex/thesis/thesis.tex

@@ -6,7 +6,7 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
-\thesisTitle{Application of Optimization Algorithms for Channel Decoding}
+\thesisTitle{Application o Optimization Algorithms for Channel Decoding}
 \thesisType{Bachelor's Thesis}
 \thesisAuthor{Andreas Tsouchlos}
 \thesisAdvisor{Prof. Dr.-Ing. Laurent Schmalen}
@@ -14,7 +14,7 @@
 \thesisSupervisor{Dr.-Ing. Holger Jäkel}
 \thesisStartDate{24.10.2022}
 \thesisEndDate{24.04.2023}
-\thesisSignatureDate{Signature date} % TODO: Signature date
+\thesisSignatureDate{24.04.2023} % TODO: Signature date
 \thesisLanguage{english}
 \setlanguage
 
@@ -35,7 +35,7 @@
 \usetikzlibrary{spy}
 \usetikzlibrary{shapes.geometric}
 \usetikzlibrary{arrows.meta,arrows}
-\tikzset{>=latex}
+\tikzset{>=stealth}
 
 \pgfplotsset{compat=newest}
 \usepgfplotslibrary{colorbrewer}