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\thesisTitle{Application of Optimization Algorithms for Channel Decoding}
\thesisType{Bachelor's Thesis}
\thesisAuthor{Andreas Tsouchlos}
\thesisAdvisor{Prof. Dr.-Ing. Laurent Schmalen}
%\thesisHeadOfInstitute{Prof. Dr.-Ing. Laurent Schmalen}
\thesisSupervisor{Dr.-Ing. Holger Jäkel}
\thesisStartDate{24.10.2022}
\thesisEndDate{24.04.2023}
\thesisSignatureDate{24.04.2023} % TODO: Signature date
\thesisLanguage{english}
\setlanguage


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\input{abbreviations.tex}

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\begin{document}

    %
    % Preliminaries
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    \pagenumbering{roman}

    \maketitle
    \makestatutorydeclaration
    %\makeCCdeclaration

    %\include{chapters/abstract}

    %
    % Main Document
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    \cleardoublepage
    \pagenumbering{arabic}


    % 1. Introduction
    %   - Problem definition
    %   - Motivation
    %   - Results summary
    %
    % 2. Theoretical Background
    %   2.2 Notation
    %       - General remarks on notation (matrices, ...)
    %       - Probabilistic quantities(random variables, PDFs, ...)
    %   2.1 Preliminaries: Channel Model and Modulation
    %       - AWGN
    %       - BPSK
    %   2.3 Channel Coding with LDPC Codes
    %       - Introduction
    %       - Binary linear codes
    %       - LDPC codes
    %   2.4 Decoding LDPC Codes using Belief Propagation
    %       - Introduction to message passing
    %       - Overview of BP algorithm
    %   2.5 Optimization Methods
    %       - ADMM
    %       - Proximal gradient method
    %   
    % 3. Decoding Techniques
    %   3.1 Decoding using Optimization Methods
    %       - General methodology
    %   3.2 LP Decoding using ADMM
    %       - Equivalent ML optimization problem
    %       - LP relaxation
    %       - ADMM as a solver
    %   3.3 Proximal Decoding
    %       - Formulation of optimization problem
    %       - Proximal gradient method as a solver
    %
    % 4. Methodology and implementation
    %   4.1 General implementation process
    %       - First python using numpy
    %       - Then C++ using Eigen
    %   4.1 LP Decoding using ADMM
    %       - Choice of parameters
    %       - Selected projection algorithm
    %       - Adaptive linear programming decoding?
    %   4.2 Proximal Decoding
    %       - Choice of parameters
    %       - Road to improved implementation
    %
    % 5. Analysis of Results
    %   5.1 LP Decoding using ADMM
    %   5.2 Proximal Decoding
    %       - Parameter choice
    %       - FER
    %       - Improved implementation
    %   5.3 Comparison of BP, Proximal Decoding and LP Decoding using ADMM
    %       - Decoding performance
    %       - Complexity & runtime (mention difficulty in reaching conclusive
    %           results when comparing implementations)
    %
    % 6. Discussion
    %   - Proximal decoding improvement limitations
    %
    % 7. Conclusion
    %   - Summary of results
    %   - Future work
   

    % Proposed new structure:
    %
    % 1. Introduction
    %
    % 2. Theoretical Background
    %   \ldots
    %
    % 3. Proximal Decoding
    %   3.1 Theory
    %   3.2 Implementation details
    %   3.3 Results
    %   3.x Improved implementation
    %
    % 4. LP Decoding using ADMM
    %   4.1 Theory
    %   4.2 Implementation details
    %   4.3 Results and comparison with proximal
    %
    % 5. Discussion
    %
    % 6. Conclusion

    \include{chapters/acknowledgements}

    \tableofcontents
    \cleardoublepage % make sure multipage TOCs are numbered correctly

    \include{chapters/introduction}
    \include{chapters/theoretical_background}
    \include{chapters/proximal_decoding}
    \include{chapters/lp_dec_using_admm}
    \include{chapters/comparison}
%    \include{chapters/discussion}
    \include{chapters/conclusion}
%    \include{chapters/appendix}


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    \addcontentsline{toc}{chapter}{List of Abbreviations}
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\end{document}