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Andreas Tsouchlos 2023-04-23 15:02:27 +02:00
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latex/thesis/chapters/introduction.tex
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\chapter{Introduction}% \chapter{Introduction}%
\label{chapter:introduction} \label{chapter:introduction}
Channel coding using binary linear codes is a way of enhancing the reliability
of data by detecting and correcting any errors that may have occurred during
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
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 performance, they are suboptimal
in most cases and exhibit a so called \textit{error floor} for high \acp{SNR},
making them unsuitable for applications with extreme reliability requiremnts.
Optimization based decoding algorithms are an entirely different way of approaching
the decoding problem, in some cases coming with stronger theoretical guarantees
and promising to alleviate the error floor issue \cite[Sec. I]{original_admm}.
\begin{itemize} This thesis aims to further the analysis of optimization based decoding
\item Problem definition algorithms as well as verify and generalize the considerations present in
\item Motivation the existing literature by considering a variety of different codes.
\begin{itemize} Specifically, the \textit{proximal decoding} \cite{proximal_paper}
\item Error floor when decoding with BP (seems to not be persent with LP decoding algorithm and \ac{LP} decoding using the \ac{ADMM} \cite{original_admm} are explored.
\cite[Sec. I]{original_admm}) The two algorithms are analyzed based on their theoretical structure
\item Strong theoretical guarantees that allow for better and better approximations and on results of simulations conducted in the scope of this work.
of ML decoding \cite[Sec. I]{original_admm} Approaches to determine the optimal value of each parameter are derived
\end{itemize} and the computational and decoding performance of the algorithms is examined.
\item Results summary An improvement on proximal decoding is suggested, offering up to $\SI{1}{dB}$
\end{itemize} of gain in decoding performance, depending on the parameters chosen and the
code considered.

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latex/thesis/chapters/lp_dec_using_admm.tex
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@ -838,9 +838,6 @@ end while
return $\tilde{\boldsymbol{c}}$ return $\tilde{\boldsymbol{c}}$
\end{genericAlgorithm} \end{genericAlgorithm}
\todo{Projection onto $[0, 1]^n$?}
\todo{Variable initialization}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Analysis and Simulation Results}% \section{Analysis and Simulation Results}%