Incorporate Lia's corrections to QM and QEC fundamentals

src/final_presentation/main.tex

@@ -302,8 +302,8 @@
         \item Quantum systems are inherently fragile
         \item Interacting with the quantum state disturbs it
         \item Idea: Represent $k\in \mathbb{N} $ \schlagwort{logical
-            qubits} using $n \in \mathbb{N},~n>k$ \schlagwort{physical qubits}
+            qubits} using $n \in \mathbb{N}$ \schlagwort{physical qubits},
-            \citereferencemanual{Rof19}
+            $n>k$ \citereferencemanual{Rof19}
 
             \vspace*{2mm}
 
@@ -1532,8 +1532,8 @@
         \item \schlagwort{Detector error model} (DEM) combines
             detector error matrix and noise model
             \visible<2->{
-            \item Tanner graph of detector error matrix of \ac{bb} code
+            \item Tanner graph of detector error matrix of bivariate
-                \citereferencemanual{KSW$^+$25}
+                bicycle (\acs{bb}) code \citereferencemanual{KSW$^+$25}
             }
     \end{itemize}
 
@@ -1549,21 +1549,25 @@
 
     \vspace*{-5mm}
 
-    \visible<3->{
+    \begin{itemize}
-        \begin{itemize}
+            \visible<2->{
             \item Challenges
-                \begin{itemize}
+            }
+            \begin{itemize}
+                    \visible<2->{
+                    \item Fault tolerance: Additional error locations \\
+                        $\implies$ \schlagwort{Increased decoding
+                        complexity} \citereferencemanual{GCR24}
+                    }
+                    \visible<3->{
                     \item Quantum setting: Degeneracy and short
                         cycles \\
                         $\implies$ \schlagwort{Degraded performance}
                         of belief propagation (BP)
                         \citereferencemanual{BBA$^+$15}
-                    \item Fault tolerance: Additional error locations \\
+                    }
-                        $\implies$ \schlagwort{Increased decoding
+            \end{itemize}
-                        complexity} \citereferencemanual{GCR24}
+    \end{itemize}
-                \end{itemize}
-        \end{itemize}
-    }
 
     \vspace*{8mm}
 
@@ -1572,9 +1576,8 @@
         S. Koutsioumpas et al., ``Automorphism ensemble decoding of
         quantum LDPC codes,'' \emph{arXiv:2503.01738}, 2025.
     }
-    {GCR24}{A. Gong, S. Cammerer, and J. M. Renes, ``Toward
+    {GCR24}{A. Gong et al., ``Toward low-latency iterative decoding
-        low-latency iterative decoding of qLDPC codes under
+        of qLDPC codes under circuit-level noise,'' arXiv:2403.18901, 2024.
-        circuit-level noise,'' arXiv:2403.18901, 2024.
     }
     {BBA$^+$15}{
         Z. Babar et al., ``Fifteen years of
@@ -1634,9 +1637,8 @@
 %     S. Huang and S. Puri, ``Improved noisy syndrome decoding of
 %     quantum LDPC codes with sliding window,'' \emph{arXiv:2311.03307}, 2023.
 % }
-% {GCR24}{A. Gong, S. Cammerer, and J. M. Renes, ``Toward
+% {GCR24}{A. Gong et al., ``Toward low-latency iterative decoding
-%     low-latency iterative decoding of qLDPC codes under
+%     of qLDPC codes under circuit-level noise,'' arXiv:2403.18901, 2024.
-%     circuit-level noise,'' arXiv:2403.18901, 2024.
 % }
 % {RWB$^+$20}{
 %     J. Roffe et al., ``Decoding across the quantum low-density
@@ -1734,9 +1736,8 @@
         S. Huang and S. Puri, ``Improved noisy syndrome decoding of
         quantum LDPC codes with sliding window,'' \emph{arXiv:2311.03307}, 2023.
     }
-    {GCR24}{A. Gong, S. Cammerer, and J. M. Renes, ``Toward
+    {GCR24}{A. Gong et al., ``Toward low-latency iterative decoding
-        low-latency iterative decoding of qLDPC codes under
+        of qLDPC codes under circuit-level noise,'' arXiv:2403.18901, 2024.
-        circuit-level noise,'' arXiv:2403.18901, 2024.
     }
     \stopreferencesmanual
 \end{frame}
@@ -2882,11 +2883,12 @@
         \vspace*{-10mm}
         \centering
         \begin{itemize}
-            \only<1>{\vspace*{10mm}}
+                \only<1>{\vspace*{10mm}}
             \item Most errors due to non-convergence
                 \vspace*{10mm}
                 \visible<2-> {
-                \item BPGD algorithm \citereferencemanual{YLH+24}
+                \item BP with guided decimation (BPGD)
+                    \citereferencemanual{YLH+24}
                     \begin{enumerate}
                         \item Perform $T$ \schlagwort{BP iterations}
                         \item Hard decision on \schlagwort{most
@@ -2906,12 +2908,12 @@
             \vspace*{-10mm}
 
             \begin{itemize}
-                \item $[[882, 24, 18 \le d \le 24]]$ - generalized
+                \item $\llbracket 882, 24, 18 \le d \le 24
-                    hypergraph product (GHP) code, \\
+                    \rrbracket$ generalized hypergraph product (GHP) code,
                     bit-flip noise \citereferencemanual{YLH+24}
             \end{itemize}
 
-            \vspace*{-5mm}
+            % \vspace*{-5mm}
 
             \begin{figure}[H]
                 \centering
@@ -2971,7 +2973,7 @@
         }
     \end{minipage}
 
-    \vspace*{2mm}
+    \vspace*{5mm}
 
     \addreferencesmanual
     {YLH+24}{Hanwen Yao et al. ``Belief propagation decoding of quantum
@@ -3329,7 +3331,7 @@
             \item Parameters
                 \begin{itemize}
                     \item $T = 1$
-                    \item $n_\text{iterations} = n$
+                    \item $n_\text{iterations} = 3{,}600$
                     \item $W = 5$
                 \end{itemize}
         \end{itemize}
@@ -3885,9 +3887,8 @@
     \vspace*{15mm}
 
     \addreferencesmanual
-    {GCR24}{A. Gong, S. Cammerer, and J. M. Renes, ``Toward
+    {GCR24}{A. Gong et al., ``Toward low-latency iterative decoding
-        low-latency iterative decoding of qLDPC codes under
+        of qLDPC codes under circuit-level noise,'' arXiv:2403.18901, 2024.
-        circuit-level noise,'' arXiv:2403.18901, 2024.
     }
     {MSL$^+$25}{
         S. Miao et al., ``Quaternary neural belief propagation
@@ -4107,9 +4108,8 @@
     \vspace*{30mm}
 
     \addreferencesmanual
-    {GCR24}{A. Gong, S. Cammerer, and J. M. Renes, ``Toward
+    {GCR24}{A. Gong et al., ``Toward low-latency iterative decoding
-        low-latency iterative decoding of qLDPC codes under
+        of qLDPC codes under circuit-level noise,'' arXiv:2403.18901, 2024.
-        circuit-level noise,'' arXiv:2403.18901, 2024.
     }
     \stopreferencesmanual
 \end{frame}
@@ -4170,9 +4170,8 @@
     \vspace*{5mm}
 
     \addreferencesmanual
-    {GCR24}{A. Gong, S. Cammerer, and J. M. Renes, ``Toward
+    {GCR24}{A. Gong et al., ``Toward low-latency iterative decoding
-        low-latency iterative decoding of qLDPC codes under
+        of qLDPC codes under circuit-level noise,'' arXiv:2403.18901, 2024.
-        circuit-level noise,'' arXiv:2403.18901, 2024.
     }
     \stopreferencesmanual
 \end{frame}

src/thesis/acronyms.tex

@@ -3,21 +3,61 @@
     long=quantum error correction
 }
 
+\DeclareAcronym{dem}{
+    short=DEM,
+    long=detector error model
+}
+
+\DeclareAcronym{ler}{
+    short=LER,
+    long=logical error rate
+}
+
 \DeclareAcronym{bp}{
     short=BP,
     long=belief propagation
 }
 
+\DeclareAcronym{bpgd}{
+    short=BPGD,
+    long=belief propagation with guided decimation
+}
+
+\DeclareAcronym{gdg}{
+    short=GDG,
+    long=guided decimation guessing
+}
+
 \DeclareAcronym{nms}{
     short=NMS,
     long=normalized min-sum
 }
 
+\DeclareAcronym{osd}{
+    short=OSD,
+    long=ordered statistics decoding
+}
+
+\DeclareAcronym{aed}{
+    short=AED,
+    long=automorphism ensemble decoding
+}
+
+\DeclareAcronym{bsc}{
+    short=BSC,
+    long=binary symetric channel
+}
+
 \DeclareAcronym{spa}{
     short=SPA,
     long=sum-product algorithm
 }
 
+\DeclareAcronym{css}{
+    short=CSS,
+    long=Calderbank-Shor-Steane
+}
+
 \DeclareAcronym{llr}{
     short=LLR,
     long=log-likelihood ratio
@@ -33,6 +73,11 @@
     long=low-density parity-check
 }
 
+\DeclareAcronym{qldpc}{
+    short=QLDPC,
+    long=quantum low-density parity-check
+}
+
 \DeclareAcronym{ml}{
     short=ML,
     long=maximum likelihood
@@ -77,3 +122,23 @@
     short=PDF,
     long=probability density function
 }
+
+\DeclareAcronym{bb}{
+    short=BB,
+    long=bivariate bicycle
+}
+
+\DeclareAcronym{hgp}{
+    short=HGP,
+    long=hypergraph product
+}
+
+\DeclareAcronym{lp}{
+    short=LP,
+    long=lifted-product
+}
+
+\DeclareAcronym{bpc}{
+    short=BPC,
+    long=balanced product code
+}

src/thesis/chapters/1_introduction.tex

@@ -1 +1,197 @@
 \chapter{Introduction}
+\label{ch:Introduction}
+
+\acresetall
+
+% Intro to quantum computing
+
+In 1982, Richard Feynman, motivated by the difficulty of simulating
+quantum-mechanical systems on classical hardware, put forward the
+idea of building computers that are themselves quantum mechanical
+\cite{feynman_simulating_1982}.
+The use of such quantum computers has since been shown to offer promising
+prospects not only with regard to simulating quantum systems but also
+for solving certain kinds of problems that are classically intractable.
+The most prominent example is Shor's algorithm for integer
+factorization \cite{shor_algorithms_1994}.
+
+Similar to the way classical computers are built from bits and gates,
+quantum computers are built from \emph{qubits} and \emph{quantum gates}.
+Because of quantum entanglement, it is not enough to consider the
+qubits individually, we also have to consider correlations between them.
+For a system of $n$ qubits, this makes the state space grow with
+$2^n$ instead of linearly with $n$, as would be the case for a classical system
+\cite[Sec.~1]{gottesman_stabilizer_1997}.
+This is both the reason quantum systems are difficult to simulate and
+what provides them with their power \cite[Sec.~2.1]{roffe_decoding_2020}.
+
+% The need for QEC
+
+Realizing algorithms that leverage these quantum-mechanical effects
+requires hardware that can execute long quantum computations reliably.
+This poses a problem, because the qubits making up current devices
+are difficult to sufficiently isolate from their environment
+\cite[Sec.~1]{roffe_quantum_2019}.
+Their interaction with the environment acts as a continuous small-scale
+measurement, an effect we call \emph{decoherence} of the stored quantum
+state.
+Decoherence is the reason large systems don't exhibit visible quantum
+properties at human scales \cite[Sec.~1]{gottesman_stabilizer_1997}.
+
+% Intro to QEC
+
+\Ac{qec} has emerged as a leading candidate in solving this problem.
+It addresses the issue by encoding the information of $k$
+\emph{logical qubits} into a larger number $n>k$ of \emph{physical
+qubits}, in close analogy to classical channel coding
+\cite[Sec.~1]{roffe_quantum_2019}.
+The redundancy introduced this way can then be used to restore
+the quantum state, should it be disturbed.
+The quantum setting imposes some important constraints that do not exist in the
+classical case, however \cite[Sec.~2.4]{roffe_quantum_2019}:
+\begin{itemize}
+    \item The no-cloning theorem prohibits the duplication of quantum states.
+    \item In addition to the bit-flip errors we know from the
+        classical setting, qubits are subject to \emph{phase-flips}.
+    \item We are not allowed to directly measure the encoded qubits,
+        as that would disturb their quantum states.
+\end{itemize}
+We can deal with the first constraint by not duplicating information, instead
+spreading the quantum state across the physical qubits
+\cite[Sec.~I]{calderbank_good_1996}.
+To deal with phase-flip errors, we must take special care when
+constructing \ac{qec} codes.
+Using \ac{css} codes, for example, we can use two separate classical
+binary linear codes to protect against the two kinds of errors
+\cite[Sec. 10.5.6]{nielsen_quantum_2010}.
+Finally, we can get around the last issue by using \emph{stabilizer
+measurements}.
+These are parity measurements that give us information about
+potential errors without revealing the underlying qubit states
+\cite[Sec.~II.C.]{babar_fifteen_2015}.
+This way, we perform a \emph{syndrome extraction} and base the
+subsequent decoding process on the measured syndrome.
+
+Another difference between \ac{qec} and classical channel coding is
+the resource constraints.
+For \ac{qec}, low latency matters more than low overall computational
+complexity, due to the backlog problem
+\cite[Sec.~II.G.3.]{terhal_quantum_2015}: Certain gates turn
+single-qubit errors into multi-qubit ones, so errors must be
+corrected beforehand.
+A \ac{qec} system that is too slow accumulates a backlog at these points,
+causing exponential slowdown.
+
+Several code constructions have been proposed for \ac{qec} codes over the years.
+Topological codes such as surface codes have been the industry
+standard for experimental applications for a long time
+\cite[Sec.~I]{koutsioumpas_colour_2025}, due to their
+reliance on only local connections between qubits
+\cite[Sec.~5]{roffe_decoding_2020}.
+Recently, \ac{qldpc} codes have been getting increasing
+attention as they have been shown to offer comparable thresholds with
+substantially improved encoding rates \cite[Sec.~1]{bravyi_high-threshold_2024}.
+\ac{qldpc} codes are generally decoded using a syndrome-based variant
+of the \ac{bp} algorithm \cite[Sec.~1]{roffe_decoding_2020}.
+We focus on \ac{qldpc} codes in our work and specifically \ac{bb} codes,
+as they are promising candidates for practical QEC due to their high
+encoding rates, large minimum distances, and short-depth syndrome
+extraction circuits \cite[Sec.~1]{bravyi_high-threshold_2024}.
+
+% DEMs and fault tolerance
+
+The syndrome extraction itself is implemented on quantum hardware and
+is therefore subject to the same noise as the data qubits.
+As a consequence, the \ac{qec} procedure, meant to protect the quantum
+state, itself introduces new \emph{internal errors}.
+A procedure is called \emph{fault-tolerant} if it remains effective
+even in the presence of these internal errors
+\cite[Sec.~4]{gottesman_introduction_2009}.
+To deal with internal errors that flip syndrome bits, multiple rounds
+of syndrome measurements are performed.
+
+One approach of implementing fault tolerance is using \acp{dem}.
+A \ac{dem} abstracts away the underlying circuit,
+focusing only on the relationship between possible errors
+and their effects on the syndrome \cite[Sec.~1.4.3]{higgott_practical_2024}.
+A \emph{detector error matrix} is generated from the circuit, which is
+used for decoding instead of the original check matrix.
+Decoding under a \ac{dem} poses a challenge with respect to the
+latency constraint.
+This is because the detector error matrix is much larger than the
+check matrix of the underlying code, since it needs to represent many
+more error locations.
+For example, in our experiments using the $\llbracket 144,12,12
+\rrbracket$ \ac{bb} code with $12$ syndrome measurement rounds, the
+number of \acp{vn} grew from $144$ to $9504$ and the number of
+\acp{cn} grew from $72$ to $1008$.
+
+To keep the latency of \ac{dem} decoding manageable, one approach is
+\emph{sliding-window decoding}.
+Instead of decoding on the entire detector error matrix at once,
+it is partitioned into several overlapping windows.
+Once decoding of one window is complete, error estimates on the initial part
+that is no longer needed are committed, and the next window is processed.
+This way, decoding can start as soon as the syndrome bits required
+for the first window have been extracted.
+The idea originates with the \emph{overlapping recovery} scheme
+proposed for the surface code in
+\cite[Sec.~IV.B]{dennis_topological_2002} and has since been studied
+for surface and toric codes \cite{kuo_fault-tolerant_2024} as well as
+for \ac{qldpc} codes under both phenomenological and circuit-level
+noise \cite{huang_increasing_2024,gong_toward_2024,kang_quits_2025}.
+
+% Reseach gap + our work
+
+We observe a structural similarity between sliding-window decoding for
+\acp{dem} and window decoding for \ac{sc}-\acs{ldpc} codes.
+In contrast to the latter, however, where \ac{bp} messages are
+carried between windows \cite[Sec.~III.~C.]{hassan_fully_2016},
+the existing realizations of sliding-window decoding for \ac{qec}
+discard the soft information produced inside one window before moving
+to the next.
+We propose \emph{warm-start sliding-window decoding}, in which the
+\ac{bp} messages from the overlap region of the previous window are
+reused to initialize \ac{bp} in the current window in place of the
+standard cold-start initialization.
+We formulate the warm start first for plain \ac{bp} and then for
+\ac{bpgd}, a variant of \ac{bp} with better convergence properties
+for \ac{qec} codes.
+The decoders are evaluated by Monte Carlo simulation on the
+$\llbracket 144,12,12 \rrbracket$ \ac{bb} code under standard
+circuit-based depolarizing noise over $12$ syndrome extraction rounds.
+The main finding is that warm-starting yields a consistent
+improvement at low iteration budgets, which is the regime relevant for
+low-latency operation.
+
+% Outline of the Thesis
+
+\Cref{ch:Fundamentals} reviews the fundamentals of classical and
+quantum error correction.
+On the classical side, it covers binary linear block codes,
+\ac{ldpc} and \ac{sc}-\ac{ldpc} codes, and the \ac{bp} decoding
+algorithm.
+On the quantum side, it introduces the relevant quantum mechanical
+notation, stabilizer measurements, stabilizer codes, \acf{css} codes,
+\ac{qldpc} codes, and the \ac{bpgd} algorithm.
+
+\Cref{ch:Fault tolerance} introduces fault-tolerant \ac{qec}.
+It formalizes the notion of fault tolerance, presents the noise
+models considered in this work, and develops the \ac{dem} formalism
+through the measurement syndrome matrix, the detector matrix, and the
+detector error matrix.
+The chapter closes with a discussion of practical considerations
+including the choice of noise model, the per-round \acf{ler}, and the
+Stim toolchain.
+
+\Cref{ch:Decoding} considers practical aspects of decoding under \acp{dem}.
+It reviews the existing literature on sliding-window decoding for
+\ac{qec}, develops the formal windowing construction we build upon,
+introduces the proposed warm-start sliding-window decoder for
+plain \ac{bp} and for \ac{bpgd}, and reports numerical results on the
+$\llbracket 144,12,12 \rrbracket$ \ac{bb} code.
+
+% TODO: Possibly extend to mention specific proposed research directions
+\Cref{ch:Conclusion} concludes the thesis and outlines directions for
+further research.
+

src/thesis/chapters/5_conclusion_and_outlook.tex

@@ -1 +1,129 @@
 \chapter{Conclusion and Outlook}
+\label{ch:Conclusion}
+
+% Recap of motivation
+
+This thesis investigated decoding under \acp{dem} for fault-tolerant
+\ac{qec}, with a focus on low-latency decoding methods for \ac{qldpc} codes.
+The repetition of the syndrome measurements, especially under
+consideration of circuit-level noise, leads to a significant increase
+in decoding complexity: in our experiments on the $\llbracket
+144,12,12 \rrbracket$ \ac{bb} code with $12$ syndrome extraction
+rounds, the check matrix grew from 144 \acp{vn} and 72
+\acp{cn} to 9504 \acp{vn} and 1008 \acp{cn}.
+
+% Recap of research gap and own work
+
+Sliding-window decoding addresses the latency constraint by
+exploiting the time-like locality of the syndrome extraction circuit,
+which manifests as a block-diagonal structure in the detector error
+matrix when detectors are defined as the difference of consecutive
+syndrome measurement rounds.
+We drew a comparison to windowed decoding for \ac{sc}-\ac{ldpc}
+codes, but noted that the existing realizations of sliding-window
+decoding discard the soft information produced inside one window
+before moving to the next.
+Building on this observation, we proposed warm-start sliding-window
+decoding, in which the \ac{bp} messages on the edges crossing into
+the overlap region of the previous window are reused to initialise
+the corresponding messages of the next window in place of the
+standard cold-start initialisation.
+
+We formulated the warm start first for plain \ac{bp} and then for
+\ac{bpgd}, the latter being attractive as an inner decoder because it
+addresses the convergence problems caused by short cycles and
+degeneracy in \ac{qldpc} Tanner graphs.
+The decoders were evaluated by Monte Carlo simulation on the
+$\llbracket 144,12,12 \rrbracket$ \ac{bb} code over $12$ syndrome
+extraction rounds under standard circuit-based depolarizing noise.
+We focused on a qualitative analysis, refraining from further
+optimizations such as introducing a normalization parameter for the
+min-sum algorithm.
+
+% Recap of experimental conclusions
+
+For plain min-sum \ac{bp}, the warm start was consistently beneficial
+across the parameter ranges we examined. The size of the gain depended
+on the overlap between consecutive windows: enlarging $W$ or
+shrinking $F$, both of which enlarge the overlap, raised the
+warm-start performance increase.
+We argued that the underlying mechanism is an effective increase in
+the number of \ac{bp} iterations spent on the \acp{vn} in the overlap
+region: each such \ac{vn} is processed by multiple consecutive window
+invocations, and the warm start lets these invocations accumulate
+iterations on the same \acp{vn} rather than restarting from scratch.
+The gain was most pronounced at low numbers of maximum iterations, where
+every additional iteration carries proportionally more information.
+
+For \ac{bpgd}, we noted that more information is available in the
+overlap region of a window: in addition to the \ac{bp} messages,
+there is information about which \acp{vn} were decimated and to what value.
+Passing this decimation information to the next window in addition to
+the messages turned out to worsen the performance considerably, which
+we attributed to a premature hard decision of the \acp{vn} in the
+overlap region.
+Restricting the warm start to the \ac{bp} messages alone, removed this effect.
+The resulting message-only warm start recovered a consistent
+improvement over cold-start that followed the same qualitative
+behaviour as for plain \ac{bp}: larger overlap, achieved by larger
+$W$ or smaller $F$, yielded a larger gain, and the
+performance difference was most pronounced at low numbers of maximum iterations.
+
+% Implications from experimental results
+
+These observations imply that the warm-start modification to
+sliding-window decoding provides a consistent improvement, as long as
+some care is taken with specifying the information to be passed to
+the subsequent window.
+Note that this comes at no additional cost to the decoding complexity,
+since the only difference between warm- and cold-start sliding-window
+decoding is the initialization of the \ac{bp} messages.
+We expect similar behavior with other inner decoders that support
+soft information initialization in the overlap region.
+
+% Further research
+
+Several directions for further research emerge from this work.
+The most immediate is an extension of the evaluation to other
+\ac{qldpc} code families, to other circuit-level noise models such as
+SI1000 or EM3, and to a range of code sizes.
+This would clarify the generality of the gain due to the warm-start
+initialization.
+We expect the qualitative findings to carry over, since the
+underlying mechanism is structural rather than code-specific, but
+quantifying the gain across code families and noise models is left to
+future work.
+
+A second direction is a systematic study of inner decoders under the
+warm-start framework.
+We considered plain min-sum \ac{bp} and \ac{bpgd}, but other
+algorithms used for \ac{qldpc} decoding, such as automorphism
+ensemble decoding \cite{koutsioumpas_automorphism_2025} or neural
+\ac{bp} \cite{miao_quaternary_2025} may admit warm-start variants of their own.
+
+A third direction is a softer treatment of the decimation state in \ac{bpgd}.
+Rather than discarding the decimation information of the previous
+window entirely, as in the message-only warm start used here, one
+could encode the decimation decisions as strong but finite biases on
+the channel \acp{llr} of the next window, allowing the new window's parity
+checks to override them if the syndrome calls for it.
+This would interpolate between the two warm-start variants studied here and
+might combine the benefits of both.
+A related question is whether the decimation schedule itself should
+be aware of the window structure, for instance by deferring
+decimation of \acp{vn} in the overlap region until they have been
+visited by the next window.
+
+A final direction is suggested by the structural similarity between
+sliding-window decoding for \acp{dem} and windowed decoding for
+\ac{sc}-\ac{ldpc} codes.
+The current approach to generating the syndrome extraction circuitry
+necessarily leads to a coupling width of one between adjacent
+syndrome measurement rounds.
+A natural question is whether the coupling width could be
+increased, e.g., by interleaving two separate realizations of the
+syndrome measurement circuitry instead of always repeating the same one.
+Work in this direction would also be a step toward bringing
+sliding-window decoding under DEMs within the scope of the analytical
+machinery developed for SC-LDPC codes.
+

src/thesis/chapters/abstract.tex

@@ -0,0 +1,56 @@
+\chapter*{Abstract}
+
+% Current state of the art
+
+\Ac{qec} protects fragile quantum states against decoherence by
+encoding logical information into a larger number of physical qubits.
+Because the syndrome extraction circuitry is itself implemented on
+noisy quantum hardware, practical \ac{qec} must be fault-tolerant,
+accounting for errors introduced by the correction procedure itself.
+Fault tolerance considerations and the syndrome extraction circuit
+are captured by \acp{dem}, which provide a unified framework for passing
+this information to the decoder.
+
+Accounting for fault tolerance substantially inflates the
+decoding problem.
+At the same time, \ac{qec} imposes strict latency constraints due to
+the backlog problem, where syndrome data accumulates faster than it
+can be decoded.
+Together, these factors pose a serious challenge for practical decoders.
+Sliding-window decoding addresses this challenge by exploiting the
+repeated structure of the syndrome extraction circuitry, partitioning
+the \ac{dem}'s check matrix into overlapping windows that can be
+decoded sequentially.
+This allows for an earlier start to the decoding process, before all
+syndrome measurements have been completed, thereby lowering the latency.
+
+% Our work: Identify research gap
+
+In this thesis, we perform a review of the existing literature on
+sliding-window decoding and draw an analogy to windowed
+decoding for classical spatially-coupled low-density parity-check
+(\acs{sc}-\acs{ldpc}) codes.
+We recognize that in contrast to the latter, existing realizations
+of sliding-window decoding for \ac{qec} discard the soft information
+produced inside one window before moving to the next.
+
+% Our work: Warm-start
+
+% TODO: Quantify improvement. Also for conclusion
+We propose warm-start sliding-window decoding, in which the
+\ac{bp} messages on the edges crossing into the overlap region of the previous
+window are reused to initialize the corresponding messages of the
+next window.
+The warm start is formulated first for plain \ac{bp} and then extended to
+\ac{bp} with guided decimation (\acs{bpgd}).
+For both plain min-sum \ac{bp} and \ac{bpgd} decoding, the warm-start
+initialization provides a consistent improvement across all examined
+parameter settings.
+We attribute this to an effective increase in \ac{bp} iterations on
+variable nodes in the overlap regions: each such VN is processed by
+multiple consecutive windows, and warm-starting lets these
+invocations accumulate iterations rather than restart from scratch.
+Crucially, the warm-start modification incurs no additional
+computational cost relative to cold-start decoding, as it differs
+only in the initialization of the \ac{bp} messages.
+

src/thesis/clean_bibliography.sh

@@ -0,0 +1,111 @@
+sed -i "s/Świerkowska/{\\\\'S}wierkowska/" bibliography.bib
+sed -i "s/Héctor/H{\\\\'e}ctor/" bibliography.bib
+sed -i "s/Bombín/Bomb{\\\\'i}n/" bibliography.bib
+sed -i "s/Zémor/Z{\\\\'e}mor/" bibliography.bib
+sed -Ezi "s/\s(abstract|note|urldate|url|keywords|file) = \{[^}]*(\{[^}]*\}[^}]*)*\},?\n//g" bibliography.bib
+
+# Normalize arXiv-only entries to @misc with howpublished = {arXiv:<id>}.
+# Detection: doi matches 10.48550/arXiv.<id>. The IEEEtranSA .bst's @article
+# handler needs a journal field (which preprints lack) and ignores publisher,
+# so for arXiv preprints we coerce the type to @misc and add howpublished
+# (the field the .bst actually prints for @misc).
+python3 - <<'PY'
+import re
+
+path = "bibliography.bib"
+with open(path) as f:
+    text = f.read()
+
+doi_re = re.compile(r"doi\s*=\s*\{10\.48550/arXiv\.([^}]+)\}")
+type_re = re.compile(r"^@([A-Za-z]+)\{", re.MULTILINE)
+howpublished_re = re.compile(r"^\s*howpublished\s*=\s*\{", re.MULTILINE)
+title_field_re = re.compile(r"\b(title|booktitle)\s*=\s*\{", re.IGNORECASE)
+inner_brace_re = re.compile(r"\{([A-Za-z0-9]+)\}")
+
+# Split into entries by scanning for top-level "@type{...}" blocks. We walk
+# brace depth so that the closing "}" of the entry is matched correctly even
+# if internal fields contain braces.
+def split_entries(s):
+    out, i, n = [], 0, len(s)
+    while i < n:
+        m = type_re.search(s, i)
+        if not m:
+            out.append(("text", s[i:]))
+            break
+        if m.start() > i:
+            out.append(("text", s[i:m.start()]))
+        depth, j = 0, m.start()
+        while j < n:
+            c = s[j]
+            if c == "{":
+                depth += 1
+            elif c == "}":
+                depth -= 1
+                if depth == 0:
+                    j += 1
+                    break
+            j += 1
+        out.append(("entry", s[m.start():j]))
+        i = j
+    return out
+
+def normalize_arxiv(entry):
+    doi_m = doi_re.search(entry)
+    if not doi_m:
+        return entry
+    arxiv_id = doi_m.group(1)
+    entry = type_re.sub("@misc{", entry, count=1)
+    if not howpublished_re.search(entry):
+        # insert howpublished as the last field, before the entry-closing "}"
+        entry = re.sub(
+            r"(,?)(\s*)\}\s*$",
+            lambda m: ("," if m.group(1) != "," else m.group(1))
+                      + m.group(2) + "\thowpublished = {arXiv:" + arxiv_id + "},\n}",
+            entry,
+            count=1,
+        )
+    return entry
+
+# Strip protective braces around words inside title/booktitle values.
+# BibTeX uses "{Word}" inside titles to preserve case against the bibliography
+# style's title-casing rules. We keep that protection only when every character
+# inside the braces is non-lowercase (e.g. acronyms like {NASA}); for ordinary
+# words like {Quantum} we drop the braces so the style's casing applies.
+def strip_title_braces(entry):
+    out, i, n = [], 0, len(entry)
+    while True:
+        m = title_field_re.search(entry, i)
+        if not m:
+            out.append(entry[i:])
+            break
+        out.append(entry[i:m.end()])
+        depth, j = 1, m.end()
+        while j < n and depth > 0:
+            c = entry[j]
+            if c == "{":
+                depth += 1
+            elif c == "}":
+                depth -= 1
+                if depth == 0:
+                    break
+            j += 1
+        value = entry[m.end():j]
+        cleaned = inner_brace_re.sub(
+            lambda mm: mm.group(1) if any(c.islower() for c in mm.group(1)) else mm.group(0),
+            value,
+        )
+        out.append(cleaned)
+        if j < n:
+            out.append(entry[j])
+        i = j + 1
+    return "".join(out)
+
+def transform(entry):
+    return strip_title_braces(normalize_arxiv(entry))
+
+parts = split_entries(text)
+new_text = "".join(transform(p) if kind == "entry" else p for kind, p in parts)
+
+with open(path, "w") as f:
+    f.write(new_text)
+PY

src/thesis/copy_sim_results.sh

@@ -0,0 +1,188 @@
+#!/bin/bash
+
+BASE_PATH="/home/andreas/workspace/private/ma-sw-results/outputs/"
+
+# Copy BP param exploration results
+
+function post_process_LERs() {
+    local filename="$1"
+
+    python3 -c "
+import pandas as pd
+import numpy as np
+
+df = pd.read_csv('${filename}')
+df['LER_per_round'] = 1 - (1 - df['LER'])**(1/12)
+df['num_errors'] = df['num_trials'] * df['LER']
+df.to_csv('${filename}', index=False)
+"       
+}
+
+i=1
+sp="/-\|"
+
+# echo "Copying BP param exploration results..."
+# echo -n ' '
+# for decoder in "WindowingSyndromeMinSumDecoder" "WindowingSyndromeSpaDecoder"; do
+#     for max_iter in 32 200 5000; do
+#         for pass_soft_info in "True" "False"; do
+#             for F in 1 2 3; do
+#                 for W in 3 4 5; do
+#                     SRC_PATH="${BASE_PATH}+rust_exp=soft_v_hard_bp,decoder.class_name=${decoder},decoder.max_iter=${max_iter},decoder.pass_soft_info=${pass_soft_info},system.F=${F},system.W=${W}/"
+#                     LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
+#                     SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
+#                     DEST_DIR="res/sim/WF/${decoder}/max_iter_${max_iter}/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}/"
+#                     mkdir -p ${DEST_DIR}
+#                     DEST_FILE="${DEST_DIR}/LERs.csv"
+#                     cp ${SRC_FILE} ${DEST_FILE}
+#                     post_process_LERs ${DEST_FILE}
+#                     printf "\b${sp:i++%${#sp}:1}"
+#                 done
+#             done
+#         done
+#     done
+# done
+#
+# # Copy BPGD param exploration results
+#
+# echo -e "\rCopying BPGD param exploration results..."
+# echo -n ' '
+# for max_iter in 32 200 5000; do
+#     for pass_soft_info in "True" "False"; do
+#         for F in 1 2 3; do
+#             for W in 3 4 5; do
+#                 SRC_PATH="${BASE_PATH}/+rust_exp=soft_v_hard_bpgd,decoder.class_name=WindowingSyndromeSpaGdDecoder,decoder.max_iter=${max_iter},decoder.pass_soft_info=${pass_soft_info},system.F=${F},system.W=${W}/"
+#                 LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
+#                 SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
+#                 DEST_DIR="res/sim/WF/WindowingSyndromeSpaGdDecoder/max_iter_${max_iter}/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}/"
+#                 mkdir -p ${DEST_DIR}
+#                 DEST_FILE="${DEST_DIR}/LERs.csv"
+#                 cp ${SRC_FILE} ${DEST_FILE}
+#                 post_process_LERs ${DEST_FILE}
+#                 printf "\b${sp:i++%${#sp}:1}"
+#             done
+#         done
+#     done
+# done
+#
+# # Copy BP over max iter. results
+#
+# echo -e "\rCopying BP over max. iter. results..."
+# echo -n ' '
+# for decoder in "WindowingSyndromeMinSumDecoder" "WindowingSyndromeSpaDecoder"; do
+#     for p in 0.001 0.0025 0.004; do
+#         for pass_soft_info in "True" "False"; do
+#             for F in 1 2 3; do
+#                 for W in 3 4 5; do
+#                     SRC_PATH="${BASE_PATH}+rust_exp=max_iter_bp,decoder.class_name=${decoder},decoder.pass_soft_info=${pass_soft_info},simulation.phy_err_rate=${p},system.F=${F},system.W=${W}/"
+#                     LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
+#                     SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
+#                     DEST_DIR="res/sim/max_iter/${decoder}/p_${p}/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}"
+#                     mkdir -p ${DEST_DIR}
+#                     DEST_FILE="${DEST_DIR}/LERs.csv"
+#                     cp ${SRC_FILE} ${DEST_FILE}
+#                     post_process_LERs ${DEST_FILE}
+#                     printf "\b${sp:i++%${#sp}:1}"
+#                 done
+#             done
+#         done
+#     done
+# done
+#
+# # Copy BPGD over max iter. results
+#
+# echo -e "\rCopying BPGD over max. iter. results..."
+# echo -n ' '
+# for p in 0.001 0.0025 0.004; do
+#     for pass_soft_info in "True" "False"; do
+#         for F in 1 2 3; do
+#             for W in 3 4 5; do
+#                 SRC_PATH="${BASE_PATH}+rust_exp=max_iter_bpgd,decoder.class_name=WindowingSyndromeSpaGdDecoder,decoder.pass_soft_info=${pass_soft_info},simulation.phy_err_rate=${p},system.F=${F},system.W=${W}/"
+#                 LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
+#                 SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
+#                 DEST_DIR="res/sim/max_iter/WindowingSyndromeSpaGdDecoder/p_${p}/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}"
+#                 mkdir -p ${DEST_DIR}
+#                 DEST_FILE="${DEST_DIR}/LERs.csv"
+#                 cp ${SRC_FILE} ${DEST_FILE}
+#                 post_process_LERs ${DEST_FILE}
+#                 printf "\b${sp:i++%${#sp}:1}"
+#             done
+#         done
+#     done
+# done
+#
+# # Copy BP over max iter. results
+#
+# echo -e "\rCopying one-shot simulation results..."
+# echo -n ' '
+# for decoder in "SyndromeMinSumDecoder" "SyndromeSpaDecoder" "SyndromeSpaGdDecoder"; do
+#     for max_iter in 32 200 5000; do
+#         SRC_PATH="${BASE_PATH}+rust_exp=whole_bp_bpgd,decoder.class_name=${decoder},decoder.max_iter=${max_iter},system.F=1,system.W=5/"
+#         LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
+#         SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
+#         DEST_DIR="res/sim/one-shot/${decoder}/max_iter_${max_iter}/"
+#         mkdir -p ${DEST_DIR}
+#         DEST_FILE="${DEST_DIR}/LERs.csv"
+#         cp ${SRC_FILE} ${DEST_FILE}
+#         post_process_LERs ${DEST_FILE}
+#         printf "\b${sp:i++%${#sp}:1}"
+#     done
+# done
+
+# Copy whole BP over max iter. results
+
+echo -e "\rCopying whole over max_iter simulation results..."
+echo -n ' '
+for decoder in "SyndromeMinSumDecoder"; do
+    for p in 0.001 0.0025 0.004; do
+        SRC_PATH="${BASE_PATH}+rust_exp=max_iter_bp,decoder.class_name=${decoder},simulation.phy_err_rate=${p}/"
+        LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
+        SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
+        DEST_DIR="res/sim/max_iter/${decoder}/p_${p}/"
+        mkdir -p ${DEST_DIR}
+        DEST_FILE="${DEST_DIR}/LERs.csv"
+        cp ${SRC_FILE} ${DEST_FILE}
+        post_process_LERs ${DEST_FILE}
+        printf "\b${sp:i++%${#sp}:1}"
+    done
+done
+
+# # Copy BPGD decimation passing
+#
+# echo -e "\rCopying BPGD param exploration results..."
+# echo -n ' '
+# for max_iter in 32 200 5000; do
+#     for F in 1 2 3; do
+#         for W in 3 4 5; do
+#             SRC_PATH="${BASE_PATH}+rust_exp=soft_v_hard_bpgd_pass_channel,decoder.class_name=WindowingSyndromeSpaGdDecoder,decoder.max_iter=${max_iter},decoder.pass_soft_info=True,system.F=${F},system.W=${W}"
+#             LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
+#             SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
+#             DEST_DIR="res/sim/WF/WindowingSyndromeSpaGdDecoderPassDecimation/max_iter_${max_iter}/pass_soft_info_True/F_${F}/W_${W}/"
+#             mkdir -p ${DEST_DIR}
+#             DEST_FILE="${DEST_DIR}/LERs.csv"
+#             cp ${SRC_FILE} ${DEST_FILE}
+#             post_process_LERs ${DEST_FILE}
+#             printf "\b${sp:i++%${#sp}:1}"
+#         done
+#     done
+# done
+
+# Copy BPGD with decimation info passing over max iter. results
+
+# echo -e "\rCopying BPGD over max. iter. results..."
+# echo -n ' '
+# for pass_soft_info in "True" "False"; do
+#     for F in 1 2 3; do
+#         for W in 3 4 5; do
+#             SRC_PATH="${BASE_PATH}+rust_exp=max_iter_bpgd_pass_channel,decoder.class_name=WindowingSyndromeSpaGdDecoder,decoder.pass_soft_info=${pass_soft_info},simulation.phy_err_rate=0.0025,system.F=${F},system.W=${W}/"
+#             LATEST_RESULTS_DIR=$(ls -t ${SRC_PATH} | head -1)
+#             SRC_FILE="${SRC_PATH}/${LATEST_RESULTS_DIR}/LERs.csv"
+#             DEST_DIR="res/sim/max_iter/WindowingSyndromeSpaGdDecoderPassDecimation/p_0.0025/pass_soft_info_${pass_soft_info}/F_${F}/W_${W}"
+#             mkdir -p ${DEST_DIR}
+#             DEST_FILE="${DEST_DIR}/LERs.csv"
+#             cp ${SRC_FILE} ${DEST_FILE}
+#             post_process_LERs ${DEST_FILE}
+#             printf "\b${sp:i++%${#sp}:1}"
+#         done
+#     done
+# done

src/thesis/main.tex

@@ -6,27 +6,44 @@
 \usepackage{amsfonts}
 \usepackage{mleftright}
 \usepackage{bm}
+\usepackage{bbm}
 \usepackage{tikz}
 \usepackage{xcolor}
 \usepackage{pgfplots}
 \pgfplotsset{compat=newest}
 \usepackage{acro}
 \usepackage{braket}
+\usepackage{listings}
+\usepackage{caption}
 % \usepackage[
 %     backend=biber,
 %     style=ieee,
 %     sorting=nty,
 % ]{biblatex}
-\usepackage{todonotes}
+% \usepackage{todonotes}
+\usepackage{quantikz}
+\usepackage{stmaryrd}
+\usepackage{algorithm}
+\usepackage[noEnd=false]{algpseudocodex}
+\usepackage{nicematrix}
+\usepackage{colortbl}
+\usepackage{cleveref}
+\usepackage{lipsum}
 
 \usetikzlibrary{calc, positioning, arrows, fit}
-
 \usetikzlibrary{external}
 \tikzexternalize
 
-\makeatletter
+% \makeatletter
-\renewcommand{\todo}[2][]{\tikzexternaldisable\@todo[#1]{#2}\tikzexternalenable}
+% \renewcommand{\todo}[2][]{\tikzexternaldisable\@todo[#1]{#2}\tikzexternalenable}
-\makeatother
+% \makeatother
+
+\setcounter{MaxMatrixCols}{20}
+
+\Crefname{equation}{}{}
+\Crefname{section}{Section}{Sections}
+\Crefname{subsection}{Subsection}{Subsections}
+\Crefname{figure}{Figure}{Figures}
 
 %
 %
@@ -35,6 +52,8 @@
 %
 
 \newcommand{\red}[1]{\textcolor{red}{#1}}
+\newcommand{\content}[1]{\noindent\indent\red{[#1]\\}}
+
 \newcommand{\figwidth}{10cm}
 \newcommand{\figheight}{7.5cm}
 
@@ -73,7 +92,9 @@
 \thesisSupervisor{Jonathan Mandelbaum}
 \thesisStartDate{01.11.2025}
 \thesisEndDate{04.05.2026}
-\thesisSignatureDate{Signature date}
+\thesisSignatureDate{04.05.2026}
+\thesisSignature{res/Unterschrift_AT_blue.png}
+\thesisSignatureHeight{2.4cm}
 \thesisLanguage{english}
 
 \begin{document}
@@ -82,7 +103,7 @@
 \maketitle
 \newpage
 
-% \include{chapters/abstract}
+\include{chapters/abstract}
 
 \cleardoublepage
 \pagenumbering{arabic}

src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_1/W_3/LERs.csv

@@ -0,0 +1,8 @@
+physical_p,num_trials,LER,LER_per_round,num_errors
+0.001,12000,0.01675,0.0014066653566989773,201.0
+0.0015,6000,0.048,0.004090796817048492,288.0
+0.002,2000,0.124,0.010971798240880681,248.0
+0.0025,2000,0.258,0.024560528611376475,516.0
+0.003,2000,0.441,0.04731136584915907,882.0
+0.0035,2000,0.6485,0.08344096230884013,1297.0
+0.004,2000,0.8085,0.1286738833656923,1617.0

src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_1/W_4/LERs.csv

@@ -0,0 +1,8 @@
+physical_p,num_trials,LER,LER_per_round,num_errors
+0.001,50000,0.004,0.0003339460107422143,200.0
+0.0015,14000,0.016,0.0013432122426282334,224.0
+0.002,6000,0.0538333333333333,0.004600762670813663,322.99999999999983
+0.0025,2000,0.1515,0.01359714508496701,303.0
+0.003,2000,0.29,0.028137416075114108,580.0
+0.0035,2000,0.485,0.05379783863208576,970.0
+0.004,2000,0.657,0.08530878077130555,1314.0

src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_1/W_5/LERs.csv

@@ -0,0 +1,8 @@
+physical_p,num_trials,LER,LER_per_round,num_errors
+0.001,74000,0.0027837837837837,0.000232278495492233,205.9999999999938
+0.0015,20000,0.01065,0.0008918618165982828,213.0
+0.002,6000,0.0386666666666666,0.003280778882142177,231.9999999999996
+0.0025,2000,0.1005,0.008787514236290539,201.0
+0.003,2000,0.2145,0.019918520513549032,429.0
+0.0035,2000,0.3975,0.041343353576980935,795.0
+0.004,2000,0.5975,0.07303396011007879,1195.0

src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_2/W_3/LERs.csv

@@ -0,0 +1,8 @@
+physical_p,num_trials,LER,LER_per_round,num_errors
+0.001,4000,0.05975,0.005120966383739489,239.0
+0.0015,2000,0.12,0.010596241035318976,240.0
+0.002,2000,0.2925,0.02842304828215303,585.0
+0.0025,2000,0.457,0.049614097064849094,914.0
+0.003,2000,0.6565,0.08519774084658893,1313.0
+0.0035,2000,0.807,0.12810716433630664,1614.0
+0.004,2000,0.927,0.19596138832598886,1854.0

src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_2/W_4/LERs.csv

@@ -0,0 +1,8 @@
+physical_p,num_trials,LER,LER_per_round,num_errors
+0.001,30000,0.0074,0.0006187681363896136,222.0
+0.0015,8000,0.027375,0.002310383366790014,219.0
+0.002,4000,0.081,0.007014379974311313,324.0
+0.0025,2000,0.1935,0.01776132322220747,387.0
+0.003,2000,0.3505,0.03532372820929974,701.0
+0.0035,2000,0.549,0.06420358199217457,1098.0
+0.004,2000,0.736,0.10504679589131227,1472.0

src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_2/W_5/LERs.csv

@@ -0,0 +1,8 @@
+physical_p,num_trials,LER,LER_per_round,num_errors
+0.001,56000,0.0035892857142857,0.0002996003321397156,200.99999999999918
+0.0015,16000,0.0141875,0.001190050056010028,227.0
+0.002,6000,0.0458333333333333,0.003902110220303623,274.99999999999983
+0.0025,2000,0.127,0.011254499159800035,254.0
+0.003,2000,0.255,0.024232483954962025,510.0
+0.0035,2000,0.455,0.049322879977013234,910.0
+0.004,2000,0.629,0.07930773938046853,1258.0

src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_3/W_3/LERs.csv

@@ -0,0 +1,8 @@
+physical_p,num_trials,LER,LER_per_round,num_errors
+0.001,2000,0.632,0.07993046327730713,1264.0
+0.0015,2000,0.7685,0.11479080536457342,1537.0
+0.002,2000,0.8905,0.16832973055592892,1781.0
+0.0025,2000,0.9405,0.2095463416012857,1881.0
+0.003,2000,0.9765,0.26843039175484296,1953.0
+0.0035,2000,0.993,0.33865993052589327,1986.0
+0.004,2000,0.995,0.3569459165824279,1990.0

src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_3/W_4/LERs.csv

@@ -0,0 +1,8 @@
+physical_p,num_trials,LER,LER_per_round,num_errors
+0.001,6000,0.0361666666666666,0.003065034000747535,216.99999999999957
+0.0015,4000,0.08675,0.007533613442062825,347.0
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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_False/F_3/W_5/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_1/W_3/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_1/W_4/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_1/W_5/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_2/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_2/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_2/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_3/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_3/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_200/pass_soft_info_True/F_3/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_1/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_1/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_1/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_2/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_2/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_2/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_3/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_3/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_False/F_3/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_1/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_1/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_1/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_2/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_2/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_2/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_3/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_3/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_32/pass_soft_info_True/F_3/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_1/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_1/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_1/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_2/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_2/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_2/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_3/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_3/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_False/F_3/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_1/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_1/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_1/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_2/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_2/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_2/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_3/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_3/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeMinSumDecoder/max_iter_5000/pass_soft_info_True/F_3/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_1/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_1/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_1/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_2/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_2/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_2/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_3/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_3/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_False/F_3/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_1/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_1/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_1/W_5/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_2/W_3/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_2/W_4/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_2/W_5/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_3/W_3/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_3/W_4/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_200/pass_soft_info_True/F_3/W_5/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_1/W_3/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_1/W_4/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_1/W_5/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_2/W_3/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_2/W_4/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_2/W_5/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_3/W_3/LERs.csv

@@ -0,0 +1,8 @@
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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_3/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_False/F_3/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_True/F_1/W_3/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_True/F_1/W_4/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_True/F_1/W_5/LERs.csv

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src/thesis/res/sim/WF/WindowingSyndromeSpaDecoder/max_iter_32/pass_soft_info_True/F_2/W_3/LERs.csv

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