Consistently capitalize character after semicolon

src/thesis/chapters/2_fundamentals.tex

@@ -193,7 +193,7 @@ decoding \cite[Preface]{ryan_channel_2009}. The iterative decoding algorithms
 are generally defined in terms of message passing on the
 \textit{Tanner graph} of a code. The Tanner graph is a bipartite
 graph that constitutes an alternative representation of the \ac{pcm}.
-We define two types of nodes: \acp{vn}, corresponding to codeword
+We define two types of nodes: \Acp{vn}, corresponding to codeword
 bits, and \acp{cn}, corresponding to individual parity checks.
 We then construct the Tanner graph by connecting each \ac{cn} to
 the \acp{vn} that make up the corresponding parity check

src/thesis/chapters/4_decoding_under_dems.tex

@@ -470,7 +470,7 @@ model and is difficult to predict beforehand.
         The block-diagonal structure reflects the time-like locality
         of the syndrome extraction circuit, with each block
         corresponding to one syndrome measurement round.
-        Two consecutive windows are highlighted: the window size $W
+        Two consecutive windows are highlighted: The window size $W
         \in \mathbb{N}$ controls the number of syndrome rounds
         included in each window, while the step size $F \in
         \mathbb{N}$ controls how many rounds separate the start of
@@ -1013,8 +1013,8 @@ the most reliable \ac{vn}, meaning we perform a hard decision and
 remove it from the following decoding process.
 
 This means that when moving from one window to the next, we now have
-more information available: not just the \ac{bp} messages but also the
-information about what \acp{vn} were decimated and to what values.
+more information available: Not just the \ac{bp} messages but also the
+Information about what \acp{vn} were decimated and to what values.
 We call this \emph{decimation information} in the following.
 We can extend \Cref{alg:warm_start_bp} by additionally passing the
 decimation information after initializing the \ac{cn} to \ac{vn} messages.
@@ -1404,7 +1404,7 @@ The fact that the $W = 5$ curve is already very close to the
 whole-block decoder indicates that the marginal benefit of enlarging
 the window saturates after a certain point.
 Thus, from a practical standpoint, the choice of $W$ represents a
-trade-off between decoding latency and accuracy: larger windows
+trade-off between decoding latency and accuracy: Larger windows
 delay the start of decoding by requiring more syndrome extraction
 rounds to be collected upfront, while the diminishing returns above
 $W = 4$ suggest that growing the window much further yields little
@@ -1511,7 +1511,7 @@ The dashed colored curves reproduce the cold-start results from
 corresponding warm-start runs for the same window sizes
 $W \in \{3, 4, 5\}$.
 The remaining experimental parameters are unchanged:
-the step size is fixed to $F = 1$,
+The step size is fixed to $F = 1$,
 the inner \ac{bp} decoder is allowed up to $200$ iterations per
 window invocation, the black curve again gives the whole-block
 reference, and the physical error rate is swept from $p = 0.001$ to
@@ -1707,7 +1707,7 @@ $n_\text{iter} \in [32, 512]$.
 
 All curves decrease monotonically with the iteration budget, but
 contrary to our expectation, none of them appears to fully saturate
-within the swept range: even at $n_\text{iter} = 4096$, every curve
+within the swept range: Even at $n_\text{iter} = 4096$, every curve
 still exhibits a noticeable downward slope.
 At $n_\text{iter} = 32$, the whole-block curve lies below both the
 $W=4$ and $W=5$ sliding-window curves.
@@ -1729,7 +1729,7 @@ mirroring the behavior already observed in \Cref{fig:whole_vs_cold_vs_warm}.
 These observations are largely consistent with the effective-iterations
 hypothesis put forward above.
 The whole-block decoder eventually overtaking every windowed scheme
-matches the prediction made there: with a sufficiently large
+matches the prediction made there: With a sufficiently large
 iteration budget, the whole-block decoder reaches an error rate
 that none of the windowed schemes can beat, because of the more global
 nature of the considered constraints.
@@ -1767,7 +1767,7 @@ sliding-window approach is still at an advantage.
 Having examined the effect of the window size $W$, we next turn to
 the second windowing parameter, the step size $F$.
 We carry out an investigation analogous to the one above:
-we first compare warm- and cold-start decoding across the full range
+We first compare warm- and cold-start decoding across the full range
 of physical error rates at a fixed iteration budget, and then we
 examine the dependence on the iteration budget at a fixed physical
 error rate.
@@ -1994,7 +1994,7 @@ At fixed $F$, the warm-start approach lies below
 cold-start across the entire sweep, and at fixed
 warm or cold start, smaller $F$ produces a lower \ac{ler}.
 Both gaps grow as the physical error rate decreases:
-the curves at $F = 1$ separate further from those at $F = 2$ and $F = 3$,
+The curves at $F = 1$ separate further from those at $F = 2$ and $F = 3$,
 and the warm-start curves separate further from the cold-start ones.
 In \Cref{fig:bp_f_over_iter}, all six curves again decrease
 monotonically with the iteration budget, with no clear saturation
@@ -2016,7 +2016,7 @@ With $W$ held fixed, decreasing $F$ enlarges the overlap between
 consecutive windows from $W - F$ to $W - F + 1$ syndrome measurement rounds, so
 a smaller step size is beneficial for the same reason that a larger
 window size is:
-each \ac{vn} in an overlap region participates in more window
+Each \ac{vn} in an overlap region participates in more window
 invocations, and the warm-start modification effectively accumulates
 iterations on it across these invocations.
 The widening of the warm/cold gap towards low iteration counts and
@@ -2281,7 +2281,7 @@ This is the opposite of what we observed for plain \ac{bp}, where
 warm-start improved upon cold-start at every parameter setting.
 The gap between the warm- and cold-start curves additionally widens
 as the physical error rate decreases:
-at the lowest sampled rate $p = 0.001$, the per-round \ac{ler} of the
+At the lowest sampled rate $p = 0.001$, the per-round \ac{ler} of the
 warm-start runs is more than two orders of magnitude above that of
 the corresponding cold-start runs.
 In \Cref{fig:bpgd_w}, larger window sizes yield lower per-round
@@ -2300,13 +2300,13 @@ than its cold-start counterpart is surprising in light of the results
 for plain \ac{bp}, where the warm-start modification was uniformly beneficial.
 The dependence on the window size in \Cref{fig:bpgd_w} is, on its own,
 consistent with the same explanation that we gave for
-\Cref{fig:whole_vs_cold}: larger windows expose the inner decoder to
+\Cref{fig:whole_vs_cold}: Larger windows expose the inner decoder to
 a larger fraction of the constraints encoded in the detector error
 matrix at the time of decoding, and this benefits both warm- and
 cold-start decoding.
 The dependence on the step size in \Cref{fig:bpgd_f}, however, is the
 opposite of the corresponding dependence under plain \ac{bp}
-(\Cref{fig:bp_f_over_p}): for warm-start, smaller $F$ now degrades performance
+(\Cref{fig:bp_f_over_p}): For warm-start, smaller $F$ now degrades performance
 rather than helps, even though smaller $F$ implies a larger overlap
 in both cases.
 
@@ -2564,7 +2564,7 @@ the warm-start curves now show a clear reordering as $n_\text{iter}$
 grows.
 At low iteration budgets the warm-start ordering matches the
 cold-start ordering, with $F = 1$ best and $F = 3$ worst, but at the
-largest iteration budget this ordering is fully inverted: warm-start
+largest iteration budget this ordering is fully inverted: Warm-start
 $F = 1$ is now the worst and $F = 3$ the best.
 
 % [Interpretation] Figure 4.11
@@ -2596,7 +2596,7 @@ decoding performance.
 The same mechanism explains the inversion of the step-size ordering
 in \Cref{fig:bpgd_iter_F}.
 At low iteration budgets, the ordering is set by the same overlap
-argument as for plain \ac{bp}: smaller $F$ implies a larger overlap
+argument as for plain \ac{bp}: Smaller $F$ implies a larger overlap
 between consecutive windows, more shared messages, and therefore
 better warm-start performance.
 At large iteration budgets, the ordering is set by the premature hard
@@ -2777,7 +2777,7 @@ since the decimation decisions were made based on the messages themselves.
 \Cref{fig:bpgd_msg} repeats the experiment of \Cref{fig:bpgd_wf}
 with the modified warm-start procedure that carries over only the
 \ac{bp} messages.
-All other experimental parameters are unchanged: the maximum number
+All other experimental parameters are unchanged: The maximum number
 of inner \ac{bp} iterations is $n_\text{iter} = 5000$, and the
 physical error rate is swept from $p = 0.001$ to $p = 0.004$ in steps
 of $0.0005$.
@@ -2810,7 +2810,7 @@ the warm-start regression observed in \Cref{fig:bpgd_wf},
 and warm-start now consistently outperforms cold-start.
 The dependence on the window size and the step size also recovers
 the qualitative behavior we observed for plain \ac{bp} in
-\Cref{fig:whole_vs_cold_vs_warm,fig:bp_f_over_p}: a larger overlap
+\Cref{fig:whole_vs_cold_vs_warm,fig:bp_f_over_p}: A larger overlap
 between consecutive windows, achieved either by enlarging $W$ or by
 decreasing $F$, both improves the absolute decoding performance and
 increases the warm-start advantage over cold-start.
@@ -2994,7 +2994,7 @@ cold-start curves across the entire range of $n_\text{iter}$ available to us.
 \Cref{fig:bpgd_msg_iter} repeats the experiment of
 \Cref{fig:bpgd_iter} with the modified warm-start procedure that
 carries over only the \ac{bp} messages.
-All other experimental parameters are unchanged: the physical error
+All other experimental parameters are unchanged: The physical error
 rate is fixed at $p = 0.0025$ and the iteration budget is swept over
 $n_\text{iter} \in \{32, 128, 256, 512, 1024, 1536, 2048, 2560,
 3072, 3584, 4096\}$.
@@ -3026,7 +3026,7 @@ initialization no longer freezes any \acp{vn} in the next window.
 The dependence of this benefit on $W$ and $F$ also recovers the
 pattern observed for plain \ac{bp} in
 \Cref{fig:whole_vs_cold_vs_warm,fig:bp_f_over_p}:
-larger overlap, achieved by larger $W$ or smaller $F$, yields more
+Larger overlap, achieved by larger $W$ or smaller $F$, yields more
 effective extra iterations and therefore a larger warm-start gain.
 
 % BPGD conclusion
@@ -3048,7 +3048,7 @@ cold-start that follows the same behavior as for plain \ac{bp} with
 regard to overlap.
 A second observation specific to \ac{bpgd} is that its iteration
 requirements are substantially larger than those of plain \ac{bp}:
-the per-round \ac{ler} drops sharply only once the iteration budget
+The per-round \ac{ler} drops sharply only once the iteration budget
 is on the order of the number of \acp{vn} in each window.
 
 Future work could include a softer treatment of the decimation state

src/thesis/chapters/5_conclusion_and_outlook.tex

@@ -7,7 +7,7 @@ This thesis investigates 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
+in decoding complexity: In our experiments on the $\llbracket
 144,12,12 \rrbracket$ \ac{bb} code with $12$ syndrome extraction
 rounds, the check matrix grows from 144 \acp{vn} and 72
 \acp{cn} to 9504 \acp{vn} and 1008 \acp{cn}.
@@ -46,18 +46,18 @@ min-sum algorithm.
 For standard min-sum \ac{bp}, the warm start is consistently
 beneficial to the cold start, across the considered parameter ranges.
 The size of the gain depends on the overlap between consecutive
-windows: enlarging $W$ or shrinking $F$, both of which enlarge the
+windows: Enlarging $W$ or shrinking $F$, both of which enlarge the
 overlap, result in larger gains of the warm-start.
 We observe 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
+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 note that more information is available in the
-overlap region of a window: in addition to the \ac{bp} messages,
+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
@@ -66,7 +66,7 @@ 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 standard \ac{bp}: larger overlap, achieved by larger
+behaviour as for standard \ac{bp}: Larger overlap, achieved by larger
 $W$ or smaller $F$, yielded a larger gain, and the
 performance difference is most pronounced at low numbers of maximum iterations.
 

src/thesis/chapters/abstract.tex

@@ -49,7 +49,7 @@ For both standard \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
+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