diff --git a/src/thesis/MA.bib b/src/thesis/bibliography.bib similarity index 100% rename from src/thesis/MA.bib rename to src/thesis/bibliography.bib diff --git a/src/thesis/chapters/2_fundamentals.tex b/src/thesis/chapters/2_fundamentals.tex index bf16aa8..16b523d 100644 --- a/src/thesis/chapters/2_fundamentals.tex +++ b/src/thesis/chapters/2_fundamentals.tex @@ -51,7 +51,7 @@ $\bm{u} \in \mathbb{F}_2^k$ of length $k \in \mathbb{N}$ (called the A measure of the amount of introduced redundancy is the \textit{code rate} $R = k/n$. We call the set of all codewords $\mathcal{C}$ the \textit{code} -\cite[Section 3.1]{ryan_channel_2009}. +\cite[Sec. 3.1]{ryan_channel_2009}. % % d_min and the [] Notation @@ -73,7 +73,7 @@ We define the \textit{minimum distance} of a code $\mathcal{C}$ as \end{align*} We can signify that a binary linear block code has information length $k$, block length $n$ and minimum distance $d_\text{min}$ using the -notation $[n,k,d_\text{dmin}]$ \cite[Section 1.3]{macwilliams_theory_1977}. +notation $[n,k,d_\text{dmin}]$ \cite[Sec. 1.3]{macwilliams_theory_1977}. % % Parity checks, H, and the syndrome @@ -88,9 +88,9 @@ additional degrees of freedom. These conditions, called parity checks, take the form of equations over $\mathbb{F}_2^n$, linking the individual positions of each codeword. We can arrange the coefficients of these equations in the -\textit{parity check matrix} (\acs{pcm}) $\bm{H} \in +\textit{parity-check matrix} (\acs{pcm}) $\bm{H} \in \mathbb{F}_2^{(n-k) \times n}$ and equivalently define the code as -\cite[Section 3.1]{ryan_channel_2009} +\cite[Sec. 3.1]{ryan_channel_2009} \begin{align*} \mathcal{C} = \left\{ \bm{x} \in \mathbb{F}_2^n : \bm{H}\bm{x}^\text{T} = \bm{0} \right\} @@ -107,7 +107,7 @@ exponentially with $n$, in contrast to keeping track of all codewords directly. % Figure \ref{fig:Diagram of a transmission system} visualizes the -entire communication process \cite[Section 1.1]{ryan_channel_2009}. +entire communication process \cite[Sec. 1.1]{ryan_channel_2009}. An input message $\bm{u}\in \mathbb{F}_2^k$ is mapped onto a codeword $\bm{x} \in \mathbb{F}_2^n$. This is passed on to a modulator, which interacts with the physical channel. @@ -120,7 +120,7 @@ This is done by first finding an estimate $\hat{\bm{x}}$ of the sent codeword and undoing the encoding. The decoding problem that we generally attempt to solve thus consists in finding the best estimate $\hat{\bm{x}}$ given $\bm{y}$. -One approach is to use the \ac{ml} criterion \cite[Section +One approach is to use the \ac{ml} criterion \cite[Sec. 1.4]{ryan_channel_2009} \begin{align*} \hat{\bm{u}}_\text{ML} = \arg\max_{\bm{x} \in \mathcal{C}} @@ -129,7 +129,7 @@ One approach is to use the \ac{ml} criterion \cite[Section \end{align*} Finally, we differentiate between \textit{soft decision} decoding, where $\bm{y} \in \mathbb{R}^n$ and \textit{hard decision} decoding, where -$\bm{y} \in \mathbb{F}_2^n$ \cite[Section 1.5.1.3]{ryan_channel_2009}. +$\bm{y} \in \mathbb{F}_2^n$ \cite[Sec. 1.5.1.3]{ryan_channel_2009}. % \begin{figure}[h] \centering diff --git a/src/thesis/main.tex b/src/thesis/main.tex index 79c80cf..23dc82d 100644 --- a/src/thesis/main.tex +++ b/src/thesis/main.tex @@ -1,4 +1,4 @@ -\documentclass[dvipsnames]{report} +\documentclass{lib/cel-thesis/cel-thesis} \usepackage[a4paper,left=3cm,right=3cm,top=2.5cm,bottom=2.5cm]{geometry} \usepackage{float} @@ -12,11 +12,11 @@ \pgfplotsset{compat=newest} \usepackage{acro} \usepackage{braket} -\usepackage[ - backend=biber, - style=ieee, - sorting=nty, -]{biblatex} +% \usepackage[ +% backend=biber, +% style=ieee, +% sorting=nty, +% ]{biblatex} \usepackage{todonotes} \usetikzlibrary{calc, positioning, arrows} @@ -36,7 +36,16 @@ % \input{acronyms.tex} -\addbibresource{src/thesis/MA.bib} + +\usepackage{babelbib} +\setlanguage + +\usepackage{caption} +\usepackage{bm} +\usepackage{subcaption} +\usepackage{todonotes} % great for draft annotations +\DeclareCaptionLabelFormat{bf-nodot}{\textbf{#1}~\textbf{#2}} +\captionsetup{labelformat=bf-nodot,labelsep=colon} % % @@ -44,23 +53,46 @@ % % -\title{Fault Tolerant Quantum Error Correction} -% \subtitle{Master's Thesis} -\author{Andreas Tsouchlos} +\thesisTitle{Fault Tolerant Quantum Error Correction} +\thesisType{Master's Thesis} +\thesisAuthor{Andreas Tsouchlos} +\thesisAdvisor{Prof. Dr.-Ing. Laurent Schmalen} +\thesisHeadOfInstitute{Prof. Dr.-Ing. Laurent Schmalen} +% \thesisHeadOfInstitute{Prof. Dr.-Ing. Peter Rost} +%\thesisHeadOfInstitute{Prof. Dr.-Ing. Peter Rost\\Prof. Dr.-Ing. +% Laurent Schmalen} +\thesisSupervisor{Jonathan Mandelbaum} +\thesisStartDate{01.11.2025} +\thesisEndDate{04.05.2026} +\thesisSignatureDate{Signature date} +\thesisLanguage{english} \begin{document} +\pagenumbering{roman} % all the preliminaries should be counted roman style \maketitle -\tableofcontents \newpage +% \include{chapters/abstract} + +\cleardoublepage +\pagenumbering{arabic} + +\tableofcontents +\cleardoublepage + \input{chapters/1_introduction.tex} \input{chapters/2_fundamentals.tex} \input{chapters/3_fault_tolerant_qec.tex} \input{chapters/4_decoding_under_dems.tex} \input{chapters/5_conclusion_and_outlook.tex} -\printbibliography +% \appendix +% \listoffigures +% \listoftables +% \include{abbreviations} + +\bibliography{lib/cel-thesis/IEEEabrv,bibliography} \end{document}