Add previous work slide; Add sliding window decoding slide
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@ -24,7 +24,7 @@
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\usepackage{tikz}
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\usepackage{tikz-3dplot}
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\usetikzlibrary{spy, external, intersections, positioning}
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\usetikzlibrary{spy, external, intersections, positioning, tikzmark}
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% \ifdefined\ishandout\else
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\tikzexternalize
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@ -47,8 +47,8 @@
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\usepackage{amssymb}
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\usepackage{acro}
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\usepackage{braket}
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% \usepackage{qcircuit}
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\usepackage{quantikz}
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\usepackage{nicematrix}
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\title{Fault Tolerant Quantum Error Correction}
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\subtitle{Master's Thesis Midterm Presentation}
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@ -103,6 +103,21 @@
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long=belief propagation
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}
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\DeclareAcronym{osd}{
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short=OSD,
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long=ordered statistics decoding,
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}
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\DeclareAcronym{qldpc}{
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short=QLDPC,
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long=quantum low density parity check,
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}
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\DeclareAcronym{scldpc}{
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short=SC-LDPC,
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long=spatially coupled low density parity check
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}
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%
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%
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% Document body
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@ -376,8 +391,8 @@
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\begin{itemize}
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\item We entangle the state with \emph{ancilla qubits} to
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perform syndrome measurements \citereference{nielsen_quantum_2010}
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\item \red{Do I need to show what the syndrome extraction
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circuitry for Z errors looks like?}
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% \item \red{Do I need to show what the syndrome extraction
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% circuitry for Z errors looks like?}
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\item Example: The 3-qubit repetition code%
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\footnote {
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Note that, for simplicity, this chosen example is a
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@ -436,7 +451,7 @@
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\begin{frame}
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\frametitle{Fault Tolerance}
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\vspace*{-15mm}
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\vspace*{-18mm}
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\begin{itemize}
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\item The quantum gates we use for syndrome extraction are
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@ -448,7 +463,7 @@
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\citereference{derks_designing_2025}
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\end{itemize}
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\vspace*{3mm}
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% \vspace*{3mm}
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\begin{figure}[H]
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\centering
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@ -472,9 +487,12 @@
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\node[above] at (internal.north) {\small QEC};
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\node[above] at (output.north) {\small Output State};
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\end{tikzpicture}
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\caption{Overview of the flow of errors in a \ac{qec} system.
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Adapted from \citereference{derks_designing_2025}.}
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\end{figure}
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\vspace*{3mm}
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% \vspace*{3mm}
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\begin{itemize}
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\item We have to modify the syndrome extraction circuitry to
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@ -484,7 +502,7 @@
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\item We generally perform multiple rounds of syndrome extraction
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\end{itemize}
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\vspace*{10mm}
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\vspace*{8mm}
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\addreferences
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{shor_fault-tolerant_1997}
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@ -971,8 +989,9 @@
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\vspace*{-17mm}
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\begin{itemize}
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\item Visualization of general process \red{Deal with 3-qubit
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state (somehow represent arbitrary qubit state)}
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\item Visualization of general process
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% \red{Deal with 3-qubit state (somehow represent arbitrary
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% qubit state)}
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\end{itemize}
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\vspace*{5mm}
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@ -1092,7 +1111,7 @@
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% tex-fmt: on
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\caption{Circuit-level noise model for the 3-qubit
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repetition code (for X errors)}
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repetition code (for X errors).}
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\end{figure}
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\end{minipage}
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@ -1107,8 +1126,15 @@
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\begin{frame}
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\frametitle{Decoding using Detector Error Models}
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% Related interesting stuff
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% - Roffe et al. use the min-sum variant of BP.
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% - Babar et al. use the SPA
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% - A lot of publications use Roffe's ldpc package -> min-sum
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\begin{itemize}
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\item A \ac{dem} combines a detector error matrix and a noise model
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\item When employing \ac{bp}, the syndrome-based variant must
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be used \citereference{babar_fifteen_2015}
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\item The likelihoods of different error locations can be
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used as priors for decoding
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\vspace*{5mm}
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@ -1138,28 +1164,150 @@
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\subsection{State of the Art}
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\label{subsec:State of the Art}
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% TODO: Mention somewhere that we are particularly interested in QLDPC codes
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\begin{frame}
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\frametitle{Sliding Window Decoding}
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\frametitle{Addressing the Challenges}
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\vspace*{-18mm}
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\begin{itemize}
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% TODO: Do I have to explain BP?
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\item \red{Do I have to explain BP}
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\item Give overview of existing research
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\item Explain exactly what they do in the main paper I am
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basing my work on
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\item \red{$\rightarrow$ We generally don't use "normal BP"
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(BP + OSD, BPGD, etc.)}
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\item Many window-based approaches exist to combat the
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decoding complexity
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\begin{itemize}
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\item Parallel decoding of syndromes
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\citereference{skoric_parallel_2023}
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\item Using sliding windows
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\citereference{huang_improved_2023}
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\citereference{gong_toward_2024}
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\end{itemize}
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\item To deal with the degraded \ac{bp} performance, it is
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usually modified or extended
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\begin{itemize}
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\item \Ac{osd} post-processing
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\citereference{roffe_decoding_2020}
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\item Guided decimation \citereference{gong_toward_2024}
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\item Neural approaches
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\citereference{kuo_exploiting_2022}
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\citereference{miao_quaternary_2025}
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\item Ensemble decoding
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\citereference{koutsioumpas_automorphism_2025}
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\end{itemize}
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\end{itemize}
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\vspace*{5mm}
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\addreferences
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{roffe_decoding_2020}
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{kuo_exploiting_2022}
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{huang_improved_2023}
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{skoric_parallel_2023}
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{gong_toward_2024}
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{miao_quaternary_2025}
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{koutsioumpas_automorphism_2025}
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\stopreferences
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\end{frame}
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\begin{frame}
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\frametitle{Guided Decimation Guessing Decoding}
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\begin{frame}[fragile]
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\frametitle{Sliding-Window Decoding}
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\vspace*{-18mm}
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\begin{itemize}
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\item Update equations
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\item Key ideas
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\item Syndrome Based BP
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\item The sliding window approach taken in
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\citereference{gong_toward_2024} resembles a \ac{scldpc}
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code decoder
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\item However, they don't pass soft information between
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windows (only update of syndrome based on hard decision
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in previous window)
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\end{itemize}
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\vspace*{-10mm}
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\begin{figure}
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\begin{subfigure}[b]{0.5\textwidth}
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\begin{gather*}
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\begin{pmatrix}
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\bm{H}_0 & \bm{H}_1 & \bm{0} & \bm{0} \\
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\bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 \\
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\bm{0} & \bm{0} & \bm{0} & \bm{H}_2
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\end{pmatrix}
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\begin{pmatrix}
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\hat{\bm{e}}_0 \\
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\hat{\bm{e}}_1 \\
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\vdots
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\end{pmatrix}
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=
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\begin{pmatrix}
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\bm{s}_1 \\
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\bm{s}_2 \\
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\bm{s}_3
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\end{pmatrix} \\[5mm]
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\bm{s}_2' = \bm{s}_2 + \bm{H}_2 \hat{\bm{e}}_1
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\end{gather*}
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\vspace*{5mm}
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\caption{Equations for the decoding of the first window}
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\end{subfigure}%
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\begin{subfigure}[b]{0.5\textwidth}
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\[
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\left(
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\begin{tikzpicture}[baseline=(m.center)]
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\matrix (m)[
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matrix of math nodes,
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nodes in empty cells,
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column sep={14mm,between origins},
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row sep={10mm,between origins},
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] {
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% tex-fmt: off
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\bm{H}_0 & \bm{H}_1 & \bm{0} & \bm{0} & \bm{0} & \bm{0} & \cdots & & \\
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\bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & \bm{0} & \bm{0} & & & \\
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\bm{0} & \bm{0} & \bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & & \phantom{\bm{0}} & \\
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\bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{H}_2 & \bm{H}_0 & \bm{H}_1 & \\
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\bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{0} & \bm{H}_2 & \\
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\vdots & \phantom{\bm{0}} & & & & & & & \ddots \\
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% tex-fmt: on
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} ;
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\draw[kit-red, line width=2pt]
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($(m-3-1.south west) + (-0.1,-0.1)$)
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rectangle
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($(m-1-4.north east) + (0.1,0.1)$);
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\draw[kit-orange, line width=2pt]
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($(m-4-3.south west) + (-0.1,-0.1)$)
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rectangle
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($(m-2-6.north east) + (0.1,0.1)$);
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\draw[kit-blue, line width=2pt]
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($(m-5-5.south west) + (-0.1,-0.1)$)
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rectangle
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($(m-3-8.north east) + (0.1,0.1)$);
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\draw[-{Latex},line width=2pt]
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($(m-1-5.north) + (0,0.8)$)
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--
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($(m-2-8.north) + (0,0.8)$);
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\end{tikzpicture}
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\right)
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\]
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\caption{Visualization of sliding window procedure}
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\end{subfigure}%
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\end{figure}
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\vspace*{-5mm}
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\begin{itemize}
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\item They try \ac{bp} + \ac{osd} and a modification of
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\ac{bp} with guided decimation
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\end{itemize}
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\vspace*{4mm}
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\addreferences
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{gong_toward_2024}
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\stopreferences
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\end{frame}
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\begin{frame}
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