32 lines
1.8 KiB
TeX
32 lines
1.8 KiB
TeX
\chapter{Introduction}%
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\label{chapter:introduction}
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Channel coding using binary linear codes is a way of enhancing the reliability
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of data by detecting and correcting any errors that may occur during
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its transmission or storage.
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One class of binary linear codes, \ac{LDPC} codes, has become especially
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popular due to being able to reach arbitrarily small probabilities of error
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at code rates up to the capacity of the channel, while retaining a structure
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that allows for very efficient decoding.
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While the established decoders for \ac{LDPC} codes, such as \ac{BP} and the
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\textit{min-sum algorithm}, offer reasonable decoding performance, they are suboptimal
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in most cases and exhibit an \textit{error floor} for high \acp{SNR},
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making them unsuitable for applications with extreme reliability requiremnts.
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Optimization based decoding algorithms are an entirely different way of approaching
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the decoding problem, in some cases coming with stronger theoretical guarantees
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and promising to alleviate the error floor issue \cite[Sec. I]{original_admm}.
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This thesis aims to further the analysis of optimization based decoding
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algorithms as well as verify and generalize the considerations present in
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the existing literature by considering a variety of different codes.
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Specifically, the \textit{proximal decoding} \cite{proximal_paper}
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algorithm and \ac{LP} decoding using the \ac{ADMM} \cite{original_admm} are explored.
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The two algorithms are analyzed based on their theoretical structure
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and based on the results of the simulations conducted in the scope of this work.
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Approaches to determine the optimal value of each parameter are derived
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and the computational and decoding performance of the algorithms is examined.
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An improvement on proximal decoding is suggested, achieving up to $\SI{1}{dB}$
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of gain, depending on the parameters chosen and the
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code considered.
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