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Added figures to proximal improvement section; Minor other changes

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Andreas Tsouchlos 2023-04-09 23:05:09 +02:00
parent 50d55af046
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17 changed files with 996 additions and 16 deletions
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4
latex/thesis/chapters/lp_dec_using_admm.tex
View File

@ -690,7 +690,7 @@ while $\sum_{j\in\mathcal{J}} \lVert \boldsymbol{T}_j\tilde{\boldsymbol{c}} - \b
\Big) - \frac{\gamma_i}{\mu} \right)$
end for
end while
\end{genericAlgorithm}
\end{genericAlgorithm}
%
\footnotetext{$\epsilon_{\text{pri}} > 0$ and $\epsilon_{\text{dual}} > 0$
are additional parameters
@ -700,7 +700,7 @@ $\boldsymbol{z}_j$ in the previous iteration.}%
%
\noindent The $\boldsymbol{z}_j$- and $\boldsymbol{\lambda}_j$-updates can be understood as
a check-node update step (lines $3$-$6$) and the $\tilde{c}_i$-updates can be understood as
a variable-node update step (lines $7$-$9$ in figure \ref{fig:lp:message_passing}).
a variable-node update step (lines $7$-$9$ in figure \ref{alg:admm}).
The updates for each variable- and check-node can be perfomed in parallel.
The main computational effort in solving the linear program then amounts to

535
latex/thesis/chapters/proximal_decoding.tex
View File

@ -246,7 +246,7 @@ return $\boldsymbol{\hat{c}}$
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Implementation Details}%
\section{Implementation Details (``A Selection of Implementation Considerations?'')}%
\label{sec:prox:Implementation Details}
The algorithm was first implemented in Python because of the fast development
@ -302,8 +302,8 @@ the gradient can be written as%
\boldsymbol{v}
,\end{align*}
%
enabling the computation of the gradient primarily with element-wise
operations and matrix-vector multiplication.
enabling its computation primarily with element-wise operations and
matrix-vector multiplication.
This is beneficial, as the libraries used for the implementation are
heavily optimized for such calculations (e.g., through vectorization of the
operations).
@ -848,14 +848,15 @@ the frame errors may largely be attributed to decoding failures.
\subsection{Convergence Properties}
\label{subsec:prox:conv_properties}
The previous observation, that the \ac{FER} arises mainly due to the
The previous observation, that the \ac{FER} may arise mainly due to the
non-convergence of the algorithm instead of convergence to the wrong codeword,
raises the question why the decoding process does not converge so often.
In figure \ref{fig:prox:convergence}, the iterative process is visualized.
In order to be able to simultaneously consider all components of the vectors
being dealt with, a BCH code with $n=7$ and $k=4$ is chosen.
Each chart shows one component of the current estimates during a given
being dealt with, a BCH code with $n=7$ and $k=4$ has been chosen.
Each chart shows one component of the current estimate during a given
iteration (alternating between $\boldsymbol{r}$ and $\boldsymbol{s}$), as well
as the gradients of the negative log-likelihood and the code-constraint
polynomial, which influence the next estimate.
@ -1271,11 +1272,35 @@ This gives rise to the notion that some property or behaviour of
$\nabla h\left( \tilde{\boldsymbol{x}} \right) $ may be related in its
magnitude to the confidence that a given bit is correct.
And indeed, the magnitude of the oscillation of
$\nabla h\left( \tilde{\boldsymbol{x}} \right)$ (introduced in a previous
section) and the probability of having a bit error are strongly correlated,
a relationship depicted in figure \ref{fig:prox:correlation}.
$\nabla h\left( \tilde{\boldsymbol{x}} \right)$ (introduced previously in
section \ref{subsec:prox:conv_properties}) and the probability of having a bit
error are strongly correlated, a relationship depicted in figure
\ref{fig:prox:correlation}.
\begin{figure}[H]
\centering
TODO: Figure
\begin{tikzpicture}
\begin{axis}[point meta min = -1,
point meta max = 1,
grid=both,
xlabel={$Var\left( \nabla h\left( \boldsymbol{x} \right) \right) $},
ylabel={Bit error (bool)},
ytick={0, 1},
width=8cm,
height=3cm,
%colormap/viridis,
scale only axis,]
\addplot [RoyalPurple, only marks,]
table [col sep=comma, x=grad_h_vars, y=bit_error]
{res/proximal/extreme_components_20433484_variance.csv};
\end{axis}
\end{tikzpicture}
\caption{Correlation between bit error and amplitude of oscillation}
\label{fig:prox:correlation}
\end{figure}
\noindent The y-axis depicts whether there is a bit error and the x-axis the
variance in $\nabla h\left( \tilde{\boldsymbol{x}} \right)$ past the iteration
@ -1289,25 +1314,179 @@ probably wrong bits, all variations of the estimate with those bits modified
can be generated.
An \ac{ML}-in-the-List step can then be performed in order to determine the
most likely candidate.
This process is outlined in figure \ref{fig:prox:improved_algorithm}.
This process is outlined in algorithm \ref{alg:prox:improved}.
Its only difference to algorithm \ref{alg:prox} is that instead of returning
the last estimate when no valid result is reached, an ML-in-the-List step is
performed (highlighted in blue).
Figure \ref{fig:prox:improved_results} shows the gain that can be achieved.
\begin{genericAlgorithm}[caption={Improved proximal decoding algorithm},
label={alg:prox:improved},]
$\boldsymbol{s} \leftarrow \boldsymbol{0}$
for $K$ iterations do
$\boldsymbol{r} \leftarrow \boldsymbol{s} - \omega \nabla L \left( \boldsymbol{y} \mid \boldsymbol{s} \right) $
$\boldsymbol{s} \leftarrow \boldsymbol{r} - \gamma \nabla h\left( \boldsymbol{r} \right) $
$\boldsymbol{\hat{x}} \leftarrow \text{sign}\left( \boldsymbol{s} \right) $
if $\boldsymbol{H}\boldsymbol{\hat{c}} = \boldsymbol{0}$
return $\boldsymbol{\hat{c}}$
end if
end for
$\textcolor{KITblue}{\text{Find }N\text{ most probably wrong bits}}$
$\textcolor{KITblue}{\text{Generate variations } \boldsymbol{\tilde{c}}_i\text{ of }\boldsymbol{\hat{c}}\text{ with the }N\text{ bits modified}}$
$\textcolor{KITblue}{\text{Compute }d_H\left( \boldsymbol{ \tilde{c}}_i, \boldsymbol{\hat{c}} \right) \text{ for all valid codewords } \boldsymbol{\tilde{c}}_i}$
$\textcolor{KITblue}{\text{Output }\boldsymbol{\tilde{c}}_i\text{ with lowest }d_H\left( \boldsymbol{ \tilde{c}}_i, \boldsymbol{\hat{c}} \right)}$
\end{genericAlgorithm}
\todo{Not hamming distance, correlation}
Figure \ref{fig:prox:improved_results} shows the gain that can be achieved,
when the number $N$ is chosen to be 12.
Again, three values of gamma are chosen, for which the \ac{BER}, \ac{FER}
and decoding failure rate is plotted.
The simulation results for the original proximal decoding algorithm are shown
with solid lines and the results for the improved version are shown with
dashed lines.
For the case of $\gamma = 0.05$, the number of frame errors produced for the
datapoints at $\SI{6}{dB}$, $\SI{6.5}{dB}$ and $\SI{7}{dB}$ are
70, 17 and 2, respectively. \todo{Redo simulation with higher number of iterations}
The gain seems to depend on the value of $\gamma$, as well as become more
pronounced for higher \ac{SNR} values.
This is to be expected, since with higher \ac{SNR} values the number of bit
errors decreases, making the correction of those errors in the ML-in-the-List
step more likely.
In figure \ref{fig:prox:improved_results_multiple} the decoding performance
In figure \ref{fig:prox:improved:comp} the decoding performance
between proximal decoding and the improved algorithm is compared for a number
of different codes.
Similar behaviour can be observed in all cases, with varying improvement over
standard proximal decoding.
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={BER},
ymode=log,
width=0.48\textwidth,
height=0.36\textwidth,
ymax=1.5, ymin=3e-8,
]
\addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=BER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={FER},
ymode=log,
width=0.48\textwidth,
height=0.36\textwidth,
ymax=1.5, ymin=3e-8,
]
\addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={Decoding Failure Rate},
ymode=log,
width=0.48\textwidth,
height=0.36\textwidth,
ymax=1.5, ymin=3e-8,
]
\addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=DFR, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[hide axis,
xmin=10, xmax=50,
ymin=0, ymax=0.4,
legend columns=3,
legend style={draw=white!15!black,legend cell align=left}]
\addlegendimage{ForestGreen, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.15$}
\addlegendimage{NavyBlue, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.01$}
\addlegendimage{RedOrange, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.05$}
\addlegendimage{Emerald, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.15$}
\addlegendimage{RoyalPurple, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.01$}
\addlegendimage{red, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.05$}
\end{axis}
\end{tikzpicture}
\caption{Simulation results for $\gamma = 0.05, \omega = 0.05, K=200, N=12$}
\label{fig:prox:improved_results}
\end{figure}
Interestingly, the improved algorithm does not have much different time
complexity than proximal decoding.
This is the case, because the ML-in-the-List step is only performed when the
@ -1317,11 +1496,339 @@ This is illustrated in figure \ref{fig:prox:time_complexity_comp}, where the
average time needed to decode a single received frame is visualized for
proximal decoding as well as for the improved algorithm.
\begin{figure}[H]
\centering
\begin{tikzpicture}
\begin{axis}[grid=both,
xlabel={$n$}, ylabel={Time per frame (s)},
legend style={at={(0.05,0.77)},anchor=south west},
legend cell align={left},]
\addplot[RedOrange, only marks, mark=*]
table [col sep=comma, x=n, y=spf]
{res/proximal/fps_vs_n.csv};
\addlegendentry{proximal}
\addplot[RoyalPurple, only marks, mark=triangle*]
table [col sep=comma, x=n, y=spf]
{res/hybrid/fps_vs_n.csv};
\addlegendentry{improved ($N = 12$)}
\end{axis}
\end{tikzpicture}
\caption{Time Complexity of Proximal Decoding and Modified Implementation%
\protect\footnotemark{}}
\label{fig:prox:time_complexity_comp}
\end{figure}%
%
\footnotetext{The datapoints depicted were calculated by evaluating the
metadata of \ac{FER} simulation results from the following codes:
BCH (31, 11); BCH (31, 26); \cite[\text{96.3.965; 204.33.484; 204.55.187;
408.33.844; PEGReg252x504}]{mackay_enc}
}%
%
In conclusion, the decoding performance of proximal decoding can be improved
by appending an ML-in-the-List step when the algorithm does not produce a
valid result.
The gain is in some cases as high as $\SI{1}{dB}$ and can be achieved with
The gain can in some cases be as high as $\SI{1}{dB}$ and is achievable with
negligible computational performance penalty.
The improvement is mainly noticable for higher \ac{SNR} values and depends on
the code as well as the chosen parameters.
\begin{figure}[H]
\centering
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={FER},
ymode=log,
legend columns=1,
legend pos=outer north east,
ymax=1.5, ymin=8e-5,
width=\textwidth,
height=0.75\textwidth,
]
\addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_963965.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_963965.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_963965.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_963965.csv};
\end{axis}
\end{tikzpicture}
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=96, k=48$ \cite[\text{96.3.965}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={FER},
ymode=log,
legend columns=1,
legend pos=outer north east,
xmin=0.5, xmax=6, xtick={1, ..., 5},
ymax=1.5, ymin=8e-5,
width=\textwidth,
height=0.75\textwidth,
]
\addplot[ForestGreen, mark=*, solid,]
table [x=SNR, y=FER, col sep=comma,
discard if not={gamma}{0.15},
discard if gt={SNR}{5.5},]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma,
discard if not={gamma}{0.15},
discard if gt={SNR}{5.5},]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma,
discard if not={gamma}{0.01},
discard if gt={SNR}{5.5},]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma,
discard if not={gamma}{0.01},
discard if gt={SNR}{5.5},]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma,
discard if not={gamma}{0.05},
discard if gt={SNR}{5.5},]
{res/proximal/2d_ber_fer_dfr_20433484.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma,
discard if not={gamma}{0.05},
discard if gt={SNR}{5.5},]
{res/hybrid/2d_ber_fer_dfr_20433484.csv};
\end{axis}
\end{tikzpicture}
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.33.484}]{mackay_enc}}
\end{subfigure}%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={FER},
ymode=log,
legend columns=1,
legend pos=outer north east,
%legend columns=2,
%legend style={at={(0.5,-0.45)},anchor=south},
ymax=1.5, ymin=8e-5,
width=\textwidth,
height=0.75\textwidth,
]
\addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_40833844.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_40833844.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_40833844.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_40833844.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_40833844.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_40833844.csv};
\end{axis}
\end{tikzpicture}
\caption{$\left( 3, 6 \right)$-regular LDPC code with $n=408, k=204$ \cite[\text{408.33.844}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={FER},
ymode=log,
legend columns=1,
legend pos=outer north east,
%legend columns=2,
%legend style={at={(0.5,-0.45)},anchor=south},
ymax=1.5, ymin=8e-5,
width=\textwidth,
height=0.75\textwidth,
]
\addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_bch_31_26.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_bch_31_26.csv};
\end{axis}
\end{tikzpicture}
\caption{BCH code with $n=31, k=26$\\[\baselineskip]}
\end{subfigure}%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={FER},
ymode=log,
legend columns=1,
legend pos=outer north east,
%legend columns=2,
%legend style={at={(0.5,-0.45)},anchor=south},
ymax=1.5, ymin=8e-5,
width=\textwidth,
height=0.75\textwidth,
]
\addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_20455187.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_20455187.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_20455187.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_20455187.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_20455187.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_20455187.csv};
\end{axis}
\end{tikzpicture}
\caption{$\left( 5, 10 \right)$-regular LDPC code with $n=204, k=102$ \cite[\text{204.55.187}]{mackay_enc}}
\end{subfigure}%
\hfill%
\begin{subfigure}[c]{0.48\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[
grid=both,
xlabel={$E_b / N_0$}, ylabel={FER},
ymode=log,
legend columns=1,
legend pos=outer north east,
ymax=1.5, ymin=8e-5,
width=\textwidth,
height=0.75\textwidth,
]
\addplot[ForestGreen, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
\addplot[Emerald, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.15}]
{res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv};
\addplot[NavyBlue, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
\addplot[RoyalPurple, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.01}]
{res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv};
\addplot[RedOrange, mark=*, solid]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/proximal/2d_ber_fer_dfr_pegreg252x504.csv};
\addplot[red, mark=triangle, densely dashed]
table [x=SNR, y=FER, col sep=comma, discard if not={gamma}{0.05}]
{res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv};
\end{axis}
\end{tikzpicture}\\
\caption{LDPC code (Progressive Edge Growth Construction) with $n=504, k=252$ \cite[\text{PEGReg252x504}]{mackay_enc}}
\end{subfigure}%
\vspace{1cm}
\begin{subfigure}[c]{\textwidth}
\centering
\begin{tikzpicture}
\begin{axis}[hide axis,
xmin=10, xmax=50,
ymin=0, ymax=0.4,
legend columns=3,
legend style={draw=white!15!black,legend cell align=left}]
\addlegendimage{ForestGreen, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.15$}
\addlegendimage{NavyBlue, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.01$}
\addlegendimage{RedOrange, mark=*, solid}
\addlegendentry{proximal, $\gamma = 0.05$}
\addlegendimage{Emerald, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.15$}
\addlegendimage{RoyalPurple, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.01$}
\addlegendimage{red, mark=triangle, densely dashed}
\addlegendentry{improved, $\gamma = 0.05$}
\end{axis}
\end{tikzpicture}
\end{subfigure}
\caption{Comparison of improvement in decoding performance for various
codes}
\label{fig:prox:improved:comp}
\end{figure}

43
latex/thesis/res/hybrid/2d_ber_fer_dfr_20433484.csv Normal file
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@ -0,0 +1,43 @@
SNR,gamma,BER,FER,DFR,num_iterations
1.0,0.01,0.08857503397398564,1.0,0.5,101.0
1.5,0.01,0.07048353321911288,0.9805825242718447,0.4950980392156863,103.0
2.0,0.01,0.05350140056022409,0.9619047619047619,0.49029126213592233,105.0
2.5,0.01,0.03744921391980215,0.9099099099099099,0.47641509433962265,111.0
3.0,0.01,0.025939542483660132,0.8416666666666667,0.45701357466063347,120.0
3.5,0.01,0.014778503994190268,0.7481481481481481,0.4279661016949153,135.0
4.0,0.01,0.00835057641146911,0.507537688442211,0.33666666666666667,199.0
4.5,0.01,0.004282382097820541,0.3754646840148699,0.27297297297297296,269.0
5.0,0.01,0.0015746260263187492,0.1931166347992352,0.16185897435897437,523.0
5.5,0.01,0.00065359477124183,0.08523206751054853,0.07853810264385692,1185.0
6.0,0.01,0.0003127631420666426,0.04130879345603272,0.0396700706991359,2445.0
6.5,0.01,0.00011029974518507847,0.015459972447573855,0.015224600542659028,6533.0
7.0,0.01,2.7036508518478465e-05,0.00452894489036366,0.004508526024462101,22301.0
7.5,0.01,8.101366552599426e-06,0.0014514830995631179,0.001449379349931836,69584.0
1.0,0.05,0.0871559633027523,0.926605504587156,0.48095238095238096,109.0
1.5,0.05,0.06592721834496511,0.8559322033898306,0.4611872146118721,118.0
2.0,0.05,0.04344614558152028,0.6917808219178082,0.4089068825910931,146.0
2.5,0.05,0.023415412676698586,0.4697674418604651,0.31962025316455694,215.0
3.0,0.05,0.010770665574814613,0.23433874709976799,0.18984962406015038,431.0
3.5,0.05,0.0049633888643176565,0.12656641604010024,0.11234705228031146,798.0
4.0,0.05,0.00151358011559054,0.045660036166365284,0.043666234327712924,2212.0
4.5,0.05,0.0003522100063308634,0.011482492041837199,0.011352141171181298,8796.0
5.0,0.05,8.711464887548632e-05,0.0030893463432539077,0.003079831676526194,32693.0
5.5,0.05,1.669054519578649e-05,0.0005991149707560712,0.000598756246924705,168582.0
6.0,0.05,3.872549019607843e-06,0.00014,0.00013998040274361588,500000.0
6.5,0.05,8.137254901960785e-07,3.4e-05,3.3998844039302665e-05,500000.0
7.0,0.05,9.80392156862745e-08,4e-06,3.9999840000639995e-06,500000.0
7.5,0.05,0.0,0.0,0.0,500000.0
1.0,0.15,0.36318190642593673,1.0,0.5,101.0
1.5,0.15,0.35721219180741604,1.0,0.5,101.0
2.0,0.15,0.3584740827023879,1.0,0.5,101.0
2.5,0.15,0.3616288099398175,1.0,0.5,101.0
3.0,0.15,0.34989529792499524,0.9805825242718447,0.4950980392156863,103.0
3.5,0.15,0.34784884827717494,0.9805825242718447,0.4950980392156863,103.0
4.0,0.15,0.3346744358120607,0.9528301886792453,0.48792270531400966,106.0
4.5,0.15,0.32926378098409176,0.9528301886792453,0.48792270531400966,106.0
5.0,0.15,0.3075335397316821,0.8859649122807017,0.4697674418604651,114.0
5.5,0.15,0.31763845889232883,0.8859649122807017,0.4697674418604651,114.0
6.0,0.15,0.2609212802768166,0.7426470588235294,0.42616033755274263,136.0
6.5,0.15,0.21796218487394958,0.6011904761904762,0.3754646840148699,168.0
7.0,0.15,0.16116533949824471,0.4410480349344978,0.30606060606060603,229.0
7.5,0.15,0.11419180852856903,0.28939828080229224,0.22444444444444445,349.0
1 SNR gamma BER FER DFR num_iterations
2 1.0 0.01 0.08857503397398564 1.0 0.5 101.0
3 1.5 0.01 0.07048353321911288 0.9805825242718447 0.4950980392156863 103.0
4 2.0 0.01 0.05350140056022409 0.9619047619047619 0.49029126213592233 105.0
5 2.5 0.01 0.03744921391980215 0.9099099099099099 0.47641509433962265 111.0
6 3.0 0.01 0.025939542483660132 0.8416666666666667 0.45701357466063347 120.0
7 3.5 0.01 0.014778503994190268 0.7481481481481481 0.4279661016949153 135.0
8 4.0 0.01 0.00835057641146911 0.507537688442211 0.33666666666666667 199.0
9 4.5 0.01 0.004282382097820541 0.3754646840148699 0.27297297297297296 269.0
10 5.0 0.01 0.0015746260263187492 0.1931166347992352 0.16185897435897437 523.0
11 5.5 0.01 0.00065359477124183 0.08523206751054853 0.07853810264385692 1185.0
12 6.0 0.01 0.0003127631420666426 0.04130879345603272 0.0396700706991359 2445.0
13 6.5 0.01 0.00011029974518507847 0.015459972447573855 0.015224600542659028 6533.0
14 7.0 0.01 2.7036508518478465e-05 0.00452894489036366 0.004508526024462101 22301.0
15 7.5 0.01 8.101366552599426e-06 0.0014514830995631179 0.001449379349931836 69584.0
16 1.0 0.05 0.0871559633027523 0.926605504587156 0.48095238095238096 109.0
17 1.5 0.05 0.06592721834496511 0.8559322033898306 0.4611872146118721 118.0
18 2.0 0.05 0.04344614558152028 0.6917808219178082 0.4089068825910931 146.0
19 2.5 0.05 0.023415412676698586 0.4697674418604651 0.31962025316455694 215.0
20 3.0 0.05 0.010770665574814613 0.23433874709976799 0.18984962406015038 431.0
21 3.5 0.05 0.0049633888643176565 0.12656641604010024 0.11234705228031146 798.0
22 4.0 0.05 0.00151358011559054 0.045660036166365284 0.043666234327712924 2212.0
23 4.5 0.05 0.0003522100063308634 0.011482492041837199 0.011352141171181298 8796.0
24 5.0 0.05 8.711464887548632e-05 0.0030893463432539077 0.003079831676526194 32693.0
25 5.5 0.05 1.669054519578649e-05 0.0005991149707560712 0.000598756246924705 168582.0
26 6.0 0.05 3.872549019607843e-06 0.00014 0.00013998040274361588 500000.0
27 6.5 0.05 8.137254901960785e-07 3.4e-05 3.3998844039302665e-05 500000.0
28 7.0 0.05 9.80392156862745e-08 4e-06 3.9999840000639995e-06 500000.0
29 7.5 0.05 0.0 0.0 0.0 500000.0
30 1.0 0.15 0.36318190642593673 1.0 0.5 101.0
31 1.5 0.15 0.35721219180741604 1.0 0.5 101.0
32 2.0 0.15 0.3584740827023879 1.0 0.5 101.0
33 2.5 0.15 0.3616288099398175 1.0 0.5 101.0
34 3.0 0.15 0.34989529792499524 0.9805825242718447 0.4950980392156863 103.0
35 3.5 0.15 0.34784884827717494 0.9805825242718447 0.4950980392156863 103.0
36 4.0 0.15 0.3346744358120607 0.9528301886792453 0.48792270531400966 106.0
37 4.5 0.15 0.32926378098409176 0.9528301886792453 0.48792270531400966 106.0
38 5.0 0.15 0.3075335397316821 0.8859649122807017 0.4697674418604651 114.0
39 5.5 0.15 0.31763845889232883 0.8859649122807017 0.4697674418604651 114.0
40 6.0 0.15 0.2609212802768166 0.7426470588235294 0.42616033755274263 136.0
41 6.5 0.15 0.21796218487394958 0.6011904761904762 0.3754646840148699 168.0
42 7.0 0.15 0.16116533949824471 0.4410480349344978 0.30606060606060603 229.0
43 7.5 0.15 0.11419180852856903 0.28939828080229224 0.22444444444444445 349.0

9
latex/thesis/res/hybrid/2d_ber_fer_dfr_20433484_metadata.json Normal file
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31
latex/thesis/res/hybrid/2d_ber_fer_dfr_20455187.csv Normal file
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@ -0,0 +1,31 @@
SNR,gamma,BER,FER,DFR,num_iterations
1.0,0.01,0.1282760629004077,1.0,0.5,101.0
1.5,0.01,0.10891089108910891,1.0,0.5,101.0
2.0,0.01,0.0815592903828198,0.9619047619047619,0.49029126213592233,105.0
2.5,0.01,0.05990286022665947,0.926605504587156,0.48095238095238096,109.0
3.0,0.01,0.03941495297305914,0.8211382113821138,0.45089285714285715,123.0
3.5,0.01,0.02159746251441753,0.5941176470588235,0.3726937269372694,170.0
4.0,0.01,0.008099504169483886,0.29022988505747127,0.22494432071269488,348.0
4.5,0.01,0.003413511153449234,0.13630229419703105,0.11995249406175772,741.0
5.0,0.01,0.0007971804984475959,0.048026628625772706,0.04582577132486389,2103.0
5.5,0.01,0.00014528144415937685,0.010614818707304257,0.01050332778702163,9515.0
1.0,0.05,0.13312948941953018,1.0,0.5,101.0
1.5,0.05,0.11264991433466591,0.9805825242718447,0.4950980392156863,103.0
2.0,0.05,0.08948390677025528,0.9528301886792453,0.48792270531400966,106.0
2.5,0.05,0.06017854296190021,0.8211382113821138,0.45089285714285715,123.0
3.0,0.05,0.03815004262574595,0.6273291925465838,0.38549618320610685,161.0
3.5,0.05,0.01944624003447533,0.36996336996337,0.2700534759358289,273.0
4.0,0.05,0.007252326217843459,0.16584564860426929,0.14225352112676057,609.0
4.5,0.05,0.0021536038238009884,0.05595567867036011,0.05299055613850997,1805.0
5.0,0.05,0.0004567736185383244,0.012752525252525253,0.01259194614137888,7920.0
5.5,0.05,5.7238650812895664e-05,0.0018341293333575463,0.0018307714617169374,55067.0
1.0,0.15,0.4978644923315861,1.0,0.5,101.0
1.5,0.15,0.5006309454474859,1.0,0.5,101.0
2.0,0.15,0.5033973985633857,1.0,0.5,101.0
2.5,0.15,0.47709182682974177,1.0,0.5,101.0
3.0,0.15,0.47005435837701415,1.0,0.5,101.0
3.5,0.15,0.4798097456804504,1.0,0.5,101.0
4.0,0.15,0.4680159192389827,1.0,0.5,101.0
4.5,0.15,0.451465734808775,1.0,0.5,101.0
5.0,0.15,0.40695981362842165,1.0,0.5,101.0
5.5,0.15,0.33649132730015086,0.9711538461538461,0.4926829268292683,104.0
1 SNR gamma BER FER DFR num_iterations
2 1.0 0.01 0.1282760629004077 1.0 0.5 101.0
3 1.5 0.01 0.10891089108910891 1.0 0.5 101.0
4 2.0 0.01 0.0815592903828198 0.9619047619047619 0.49029126213592233 105.0
5 2.5 0.01 0.05990286022665947 0.926605504587156 0.48095238095238096 109.0
6 3.0 0.01 0.03941495297305914 0.8211382113821138 0.45089285714285715 123.0
7 3.5 0.01 0.02159746251441753 0.5941176470588235 0.3726937269372694 170.0
8 4.0 0.01 0.008099504169483886 0.29022988505747127 0.22494432071269488 348.0
9 4.5 0.01 0.003413511153449234 0.13630229419703105 0.11995249406175772 741.0
10 5.0 0.01 0.0007971804984475959 0.048026628625772706 0.04582577132486389 2103.0
11 5.5 0.01 0.00014528144415937685 0.010614818707304257 0.01050332778702163 9515.0
12 1.0 0.05 0.13312948941953018 1.0 0.5 101.0
13 1.5 0.05 0.11264991433466591 0.9805825242718447 0.4950980392156863 103.0
14 2.0 0.05 0.08948390677025528 0.9528301886792453 0.48792270531400966 106.0
15 2.5 0.05 0.06017854296190021 0.8211382113821138 0.45089285714285715 123.0
16 3.0 0.05 0.03815004262574595 0.6273291925465838 0.38549618320610685 161.0
17 3.5 0.05 0.01944624003447533 0.36996336996337 0.2700534759358289 273.0
18 4.0 0.05 0.007252326217843459 0.16584564860426929 0.14225352112676057 609.0
19 4.5 0.05 0.0021536038238009884 0.05595567867036011 0.05299055613850997 1805.0
20 5.0 0.05 0.0004567736185383244 0.012752525252525253 0.01259194614137888 7920.0
21 5.5 0.05 5.7238650812895664e-05 0.0018341293333575463 0.0018307714617169374 55067.0
22 1.0 0.15 0.4978644923315861 1.0 0.5 101.0
23 1.5 0.15 0.5006309454474859 1.0 0.5 101.0
24 2.0 0.15 0.5033973985633857 1.0 0.5 101.0
25 2.5 0.15 0.47709182682974177 1.0 0.5 101.0
26 3.0 0.15 0.47005435837701415 1.0 0.5 101.0
27 3.5 0.15 0.4798097456804504 1.0 0.5 101.0
28 4.0 0.15 0.4680159192389827 1.0 0.5 101.0
29 4.5 0.15 0.451465734808775 1.0 0.5 101.0
30 5.0 0.15 0.40695981362842165 1.0 0.5 101.0
31 5.5 0.15 0.33649132730015086 0.9711538461538461 0.4926829268292683 104.0

9
latex/thesis/res/hybrid/2d_ber_fer_dfr_20455187_metadata.json Normal file
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31
latex/thesis/res/hybrid/2d_ber_fer_dfr_40833844.csv Normal file
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@ -0,0 +1,31 @@
SNR,gamma,BER,FER,DFR,num_iterations
1.0,0.01,0.0918025626092021,1.0,0.5,101.0
1.5,0.01,0.07178217821782178,1.0,0.5,101.0
2.0,0.01,0.05319355464958261,1.0,0.5,101.0
2.5,0.01,0.037701845444059974,0.9901960784313726,0.4975369458128079,102.0
3.0,0.01,0.024914334665905195,0.9805825242718447,0.4950980392156863,103.0
3.5,0.01,0.014256161180068358,0.926605504587156,0.48095238095238096,109.0
4.0,0.01,0.00819607843137255,0.808,0.4469026548672566,125.0
4.5,0.01,0.003703703703703704,0.5611111111111111,0.3594306049822064,180.0
5.0,0.01,0.0017734056079769791,0.3447098976109215,0.2563451776649746,293.0
5.5,0.01,0.0007903353279891611,0.19385796545105566,0.16237942122186494,521.0
1.0,0.05,0.08972510572856593,0.9901960784313726,0.4975369458128079,102.0
1.5,0.05,0.06624649859943978,0.9619047619047619,0.49029126213592233,105.0
2.0,0.05,0.04635172653132049,0.8938053097345132,0.4719626168224299,113.0
2.5,0.05,0.024525719378660556,0.6558441558441559,0.396078431372549,154.0
3.0,0.05,0.010826771653543307,0.39763779527559057,0.28450704225352114,254.0
3.5,0.05,0.004023473188558577,0.18100358422939067,0.15326251896813353,558.0
4.0,0.05,0.0010486080573690086,0.05807935595169638,0.05489130434782609,1739.0
4.5,0.05,0.00020709882532053673,0.012814006597310327,0.01265188525616936,7882.0
5.0,0.05,3.131208430508767e-05,0.002224669603524229,0.0022197314344739676,45400.0
5.5,0.05,6.4252223396991424e-06,0.00046369625599706175,0.00046348134143431416,217815.0
1.0,0.15,0.3438895360124248,1.0,0.5,101.0
1.5,0.15,0.34032226752086975,1.0,0.5,101.0
2.0,0.15,0.33034847602407297,1.0,0.5,101.0
2.5,0.15,0.32974179770918266,1.0,0.5,101.0
3.0,0.15,0.3295476606484178,1.0,0.5,101.0
3.5,0.15,0.32175791108522617,1.0,0.5,101.0
4.0,0.15,0.3154241894777713,1.0,0.5,101.0
4.5,0.15,0.32195204814599104,1.0,0.5,101.0
5.0,0.15,0.3212483013007183,1.0,0.5,101.0
5.5,0.15,0.31752210688196847,0.9901960784313726,0.4975369458128079,102.0
1 SNR gamma BER FER DFR num_iterations
2 1.0 0.01 0.0918025626092021 1.0 0.5 101.0
3 1.5 0.01 0.07178217821782178 1.0 0.5 101.0
4 2.0 0.01 0.05319355464958261 1.0 0.5 101.0
5 2.5 0.01 0.037701845444059974 0.9901960784313726 0.4975369458128079 102.0
6 3.0 0.01 0.024914334665905195 0.9805825242718447 0.4950980392156863 103.0
7 3.5 0.01 0.014256161180068358 0.926605504587156 0.48095238095238096 109.0
8 4.0 0.01 0.00819607843137255 0.808 0.4469026548672566 125.0
9 4.5 0.01 0.003703703703703704 0.5611111111111111 0.3594306049822064 180.0
10 5.0 0.01 0.0017734056079769791 0.3447098976109215 0.2563451776649746 293.0
11 5.5 0.01 0.0007903353279891611 0.19385796545105566 0.16237942122186494 521.0
12 1.0 0.05 0.08972510572856593 0.9901960784313726 0.4975369458128079 102.0
13 1.5 0.05 0.06624649859943978 0.9619047619047619 0.49029126213592233 105.0
14 2.0 0.05 0.04635172653132049 0.8938053097345132 0.4719626168224299 113.0
15 2.5 0.05 0.024525719378660556 0.6558441558441559 0.396078431372549 154.0
16 3.0 0.05 0.010826771653543307 0.39763779527559057 0.28450704225352114 254.0
17 3.5 0.05 0.004023473188558577 0.18100358422939067 0.15326251896813353 558.0
18 4.0 0.05 0.0010486080573690086 0.05807935595169638 0.05489130434782609 1739.0
19 4.5 0.05 0.00020709882532053673 0.012814006597310327 0.01265188525616936 7882.0
20 5.0 0.05 3.131208430508767e-05 0.002224669603524229 0.0022197314344739676 45400.0
21 5.5 0.05 6.4252223396991424e-06 0.00046369625599706175 0.00046348134143431416 217815.0
22 1.0 0.15 0.3438895360124248 1.0 0.5 101.0
23 1.5 0.15 0.34032226752086975 1.0 0.5 101.0
24 2.0 0.15 0.33034847602407297 1.0 0.5 101.0
25 2.5 0.15 0.32974179770918266 1.0 0.5 101.0
26 3.0 0.15 0.3295476606484178 1.0 0.5 101.0
27 3.5 0.15 0.32175791108522617 1.0 0.5 101.0
28 4.0 0.15 0.3154241894777713 1.0 0.5 101.0
29 4.5 0.15 0.32195204814599104 1.0 0.5 101.0
30 5.0 0.15 0.3212483013007183 1.0 0.5 101.0
31 5.5 0.15 0.31752210688196847 0.9901960784313726 0.4975369458128079 102.0

9
latex/thesis/res/hybrid/2d_ber_fer_dfr_40833844_metadata.json Normal file
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@ -0,0 +1,9 @@
{
"duration": 871.6730747620168,
"name": "2d_BER_FER_DFR_40833844",
"platform": "Linux-6.1.6-arch1-3-x86_64-with-glibc2.36",
"omega": 0.05,
"K": 200,
"min_var_k": 150,
"end_time": "2023-01-24 09:12:00.353386"
}

31
latex/thesis/res/hybrid/2d_ber_fer_dfr_963965.csv Normal file
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@ -0,0 +1,31 @@
SNR,gamma,BER,FER,DFR,num_iterations
1.0,0.01,0.0943452380952381,0.9619047619047619,0.49029126213592233,105.0
1.5,0.01,0.07425458715596331,0.926605504587156,0.48095238095238096,109.0
2.0,0.01,0.05845385674931129,0.8347107438016529,0.45248868778280543,121.0
2.5,0.01,0.04104938271604938,0.7481481481481481,0.425531914893617,135.0
3.0,0.01,0.02481785063752277,0.5519125683060109,0.35563380281690143,183.0
3.5,0.01,0.01668552036199095,0.45701357466063347,0.3136645962732919,221.0
4.0,0.01,0.009225217864923748,0.3300653594771242,0.24815724815724816,306.0
4.5,0.01,0.0038886542792792795,0.17060810810810811,0.14574314574314573,592.0
5.0,0.01,0.0018921095008051529,0.09758454106280193,0.08890845070422536,1035.0
5.5,0.01,0.0008550995024875622,0.04710820895522388,0.04498886414253898,2144.0
1.0,0.05,0.09079861111111111,0.8416666666666667,0.45701357466063347,120.0
1.5,0.05,0.06677704194260485,0.6688741721854304,0.396,151.0
2.0,0.05,0.050011510128913444,0.5580110497237569,0.3489208633093525,181.0
2.5,0.05,0.03151611922141119,0.3686131386861314,0.26541554959785524,274.0
3.0,0.05,0.01758841234010534,0.22799097065462753,0.18265682656826568,443.0
3.5,0.05,0.006907068532472192,0.10871905274488698,0.09365853658536585,929.0
4.0,0.05,0.003318484521238301,0.05453563714902808,0.04879301489470981,1852.0
4.5,0.05,0.0010753547719105914,0.018454229855655035,0.01794365691727974,5473.0
5.0,0.05,0.0003437132188806364,0.006148788506027031,0.005629880743386404,16426.0
5.5,0.05,9.290550348976298e-05,0.0017593979723373864,0.0016521451800838246,57406.0
1.0,0.15,0.399236798679868,1.0,0.5,101.0
1.5,0.15,0.38721955128205127,0.9711538461538461,0.4926829268292683,104.0
2.0,0.15,0.3641141141141141,0.9099099099099099,0.47393364928909953,111.0
2.5,0.15,0.34692028985507245,0.8782608695652174,0.4675925925925926,115.0
3.0,0.15,0.31012139107611547,0.7952755905511811,0.44052863436123346,127.0
3.5,0.15,0.2872767857142857,0.7214285714285714,0.41422594142259417,140.0
4.0,0.15,0.23815104166666667,0.63125,0.3798449612403101,160.0
4.5,0.15,0.2106729055258467,0.5401069518716578,0.34843205574912894,187.0
5.0,0.15,0.19948186528497408,0.5233160621761658,0.3412969283276451,193.0
5.5,0.15,0.17773729446935724,0.452914798206278,0.3117283950617284,223.0
1 SNR gamma BER FER DFR num_iterations
2 1.0 0.01 0.0943452380952381 0.9619047619047619 0.49029126213592233 105.0
3 1.5 0.01 0.07425458715596331 0.926605504587156 0.48095238095238096 109.0
4 2.0 0.01 0.05845385674931129 0.8347107438016529 0.45248868778280543 121.0
5 2.5 0.01 0.04104938271604938 0.7481481481481481 0.425531914893617 135.0
6 3.0 0.01 0.02481785063752277 0.5519125683060109 0.35563380281690143 183.0
7 3.5 0.01 0.01668552036199095 0.45701357466063347 0.3136645962732919 221.0
8 4.0 0.01 0.009225217864923748 0.3300653594771242 0.24815724815724816 306.0
9 4.5 0.01 0.0038886542792792795 0.17060810810810811 0.14574314574314573 592.0
10 5.0 0.01 0.0018921095008051529 0.09758454106280193 0.08890845070422536 1035.0
11 5.5 0.01 0.0008550995024875622 0.04710820895522388 0.04498886414253898 2144.0
12 1.0 0.05 0.09079861111111111 0.8416666666666667 0.45701357466063347 120.0
13 1.5 0.05 0.06677704194260485 0.6688741721854304 0.396 151.0
14 2.0 0.05 0.050011510128913444 0.5580110497237569 0.3489208633093525 181.0
15 2.5 0.05 0.03151611922141119 0.3686131386861314 0.26541554959785524 274.0
16 3.0 0.05 0.01758841234010534 0.22799097065462753 0.18265682656826568 443.0
17 3.5 0.05 0.006907068532472192 0.10871905274488698 0.09365853658536585 929.0
18 4.0 0.05 0.003318484521238301 0.05453563714902808 0.04879301489470981 1852.0
19 4.5 0.05 0.0010753547719105914 0.018454229855655035 0.01794365691727974 5473.0
20 5.0 0.05 0.0003437132188806364 0.006148788506027031 0.005629880743386404 16426.0
21 5.5 0.05 9.290550348976298e-05 0.0017593979723373864 0.0016521451800838246 57406.0
22 1.0 0.15 0.399236798679868 1.0 0.5 101.0
23 1.5 0.15 0.38721955128205127 0.9711538461538461 0.4926829268292683 104.0
24 2.0 0.15 0.3641141141141141 0.9099099099099099 0.47393364928909953 111.0
25 2.5 0.15 0.34692028985507245 0.8782608695652174 0.4675925925925926 115.0
26 3.0 0.15 0.31012139107611547 0.7952755905511811 0.44052863436123346 127.0
27 3.5 0.15 0.2872767857142857 0.7214285714285714 0.41422594142259417 140.0
28 4.0 0.15 0.23815104166666667 0.63125 0.3798449612403101 160.0
29 4.5 0.15 0.2106729055258467 0.5401069518716578 0.34843205574912894 187.0
30 5.0 0.15 0.19948186528497408 0.5233160621761658 0.3412969283276451 193.0
31 5.5 0.15 0.17773729446935724 0.452914798206278 0.3117283950617284 223.0

9
latex/thesis/res/hybrid/2d_ber_fer_dfr_963965_metadata.json Normal file
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@ -0,0 +1,9 @@
{
"duration": 12.159791988000507,
"name": "2d_BER_FER_DFR_963965",
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"omega": 0.05,
"K": 200,
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"end_time": "2023-01-24 09:16:22.859899"
}

31
latex/thesis/res/hybrid/2d_ber_fer_dfr_bch_31_26.csv Normal file
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@ -0,0 +1,31 @@
SNR,gamma,BER,FER,DFR,num_iterations
1.0,0.01,0.1076036866359447,0.7214285714285714,0.014084507042253521,140.0
1.5,0.01,0.09863523573200993,0.6474358974358975,0.006369426751592357,156.0
2.0,0.01,0.06782464846980976,0.517948717948718,0.01015228426395939,195.0
2.5,0.01,0.05789547823637132,0.4410480349344978,0.01293103448275862,229.0
3.0,0.01,0.040507667900581704,0.33114754098360655,0.022435897435897436,305.0
3.5,0.01,0.03225806451612903,0.24634146341463414,0.0024330900243309003,410.0
4.0,0.01,0.021353930031803726,0.17781690140845072,0.01217391304347826,568.0
4.5,0.01,0.013437889859205132,0.11160220994475138,0.006586169045005488,905.0
5.0,0.01,0.0063573012906718825,0.05468327016783974,0.0021609940572663426,1847.0
5.5,0.01,0.0027177400481643932,0.023636789141118653,0.00046783625730994154,4273.0
1.0,0.05,0.08720083246618106,0.6516129032258065,0.00641025641025641,155.0
1.5,0.05,0.0712799167533819,0.543010752688172,0.0053475935828877,186.0
2.0,0.05,0.06328137058187992,0.48325358851674644,0.0,209.0
2.5,0.05,0.04130340017436791,0.34121621621621623,0.010033444816053512,296.0
3.0,0.05,0.02823529411764706,0.2376470588235294,0.009324009324009324,425.0
3.5,0.05,0.021330060776063583,0.18297101449275363,0.0018083182640144665,552.0
4.0,0.05,0.014593883328681367,0.12484548825710753,0.0,809.0
4.5,0.05,0.006654567453115548,0.06110102843315184,0.0006045949214026602,1653.0
5.0,0.05,0.0034803386837047425,0.032528180354267314,0.0003219575016097875,3105.0
5.5,0.05,0.0017559403087039132,0.01671078755790867,0.000496113775425831,6044.0
1.0,0.15,0.31174587540014775,0.7709923664122137,0.0,131.0
1.5,0.15,0.32302867383512546,0.7013888888888888,0.0,144.0
2.0,0.15,0.2903225806451613,0.6474358974358975,0.012658227848101266,156.0
2.5,0.15,0.20661703887510338,0.517948717948718,0.00510204081632653,195.0
3.0,0.15,0.20477476197243144,0.44493392070484583,0.0043859649122807015,227.0
3.5,0.15,0.14526953886122537,0.3389261744966443,0.0,298.0
4.0,0.15,0.1234954260953298,0.2512437810945274,0.0024813895781637717,402.0
4.5,0.15,0.09664719329438659,0.19881889763779528,0.0,508.0
5.0,0.15,0.055768179332968834,0.10699152542372882,0.0,944.0
5.5,0.15,0.0412538327040519,0.0793401413982718,0.0,1273.0
1 SNR gamma BER FER DFR num_iterations
2 1.0 0.01 0.1076036866359447 0.7214285714285714 0.014084507042253521 140.0
3 1.5 0.01 0.09863523573200993 0.6474358974358975 0.006369426751592357 156.0
4 2.0 0.01 0.06782464846980976 0.517948717948718 0.01015228426395939 195.0
5 2.5 0.01 0.05789547823637132 0.4410480349344978 0.01293103448275862 229.0
6 3.0 0.01 0.040507667900581704 0.33114754098360655 0.022435897435897436 305.0
7 3.5 0.01 0.03225806451612903 0.24634146341463414 0.0024330900243309003 410.0
8 4.0 0.01 0.021353930031803726 0.17781690140845072 0.01217391304347826 568.0
9 4.5 0.01 0.013437889859205132 0.11160220994475138 0.006586169045005488 905.0
10 5.0 0.01 0.0063573012906718825 0.05468327016783974 0.0021609940572663426 1847.0
11 5.5 0.01 0.0027177400481643932 0.023636789141118653 0.00046783625730994154 4273.0
12 1.0 0.05 0.08720083246618106 0.6516129032258065 0.00641025641025641 155.0
13 1.5 0.05 0.0712799167533819 0.543010752688172 0.0053475935828877 186.0
14 2.0 0.05 0.06328137058187992 0.48325358851674644 0.0 209.0
15 2.5 0.05 0.04130340017436791 0.34121621621621623 0.010033444816053512 296.0
16 3.0 0.05 0.02823529411764706 0.2376470588235294 0.009324009324009324 425.0
17 3.5 0.05 0.021330060776063583 0.18297101449275363 0.0018083182640144665 552.0
18 4.0 0.05 0.014593883328681367 0.12484548825710753 0.0 809.0
19 4.5 0.05 0.006654567453115548 0.06110102843315184 0.0006045949214026602 1653.0
20 5.0 0.05 0.0034803386837047425 0.032528180354267314 0.0003219575016097875 3105.0
21 5.5 0.05 0.0017559403087039132 0.01671078755790867 0.000496113775425831 6044.0
22 1.0 0.15 0.31174587540014775 0.7709923664122137 0.0 131.0
23 1.5 0.15 0.32302867383512546 0.7013888888888888 0.0 144.0
24 2.0 0.15 0.2903225806451613 0.6474358974358975 0.012658227848101266 156.0
25 2.5 0.15 0.20661703887510338 0.517948717948718 0.00510204081632653 195.0
26 3.0 0.15 0.20477476197243144 0.44493392070484583 0.0043859649122807015 227.0
27 3.5 0.15 0.14526953886122537 0.3389261744966443 0.0 298.0
28 4.0 0.15 0.1234954260953298 0.2512437810945274 0.0024813895781637717 402.0
29 4.5 0.15 0.09664719329438659 0.19881889763779528 0.0 508.0
30 5.0 0.15 0.055768179332968834 0.10699152542372882 0.0 944.0
31 5.5 0.15 0.0412538327040519 0.0793401413982718 0.0 1273.0

9
latex/thesis/res/hybrid/2d_ber_fer_dfr_bch_31_26_metadata.json Normal file
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@ -0,0 +1,9 @@
{
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"end_time": "2023-01-24 16:51:03.263440"
}

31
latex/thesis/res/hybrid/2d_ber_fer_dfr_pegreg252x504.csv Normal file
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@ -0,0 +1,31 @@
SNR,gamma,BER,FER,DFR,num_iterations
1.0,0.01,0.09354864057834354,1.0,0.5,101.0
1.5,0.01,0.07331447430457332,1.0,0.5,101.0
2.0,0.01,0.05638063806380638,1.0,0.5,101.0
2.5,0.01,0.040782649693540785,1.0,0.5,101.0
3.0,0.01,0.024859943977591035,0.9901960784313726,0.4975369458128079,102.0
3.5,0.01,0.01549865229110512,0.9528301886792453,0.48792270531400966,106.0
4.0,0.01,0.008361678004535147,0.9017857142857143,0.47417840375586856,112.0
4.5,0.01,0.003981570256738042,0.6778523489932886,0.404,149.0
5.0,0.01,0.001657329598506069,0.396078431372549,0.28370786516853935,255.0
5.5,0.01,0.00063619302096256,0.20240480961923848,0.16833333333333333,499.0
1.0,0.05,0.09390224736759391,1.0,0.5,101.0
1.5,0.05,0.06728351406569229,1.0,0.5,101.0
2.0,0.05,0.04523809523809524,0.9619047619047619,0.49029126213592233,105.0
2.5,0.05,0.02620517342739565,0.7481481481481481,0.4279661016949153,135.0
3.0,0.05,0.010427855352667383,0.37969924812030076,0.27520435967302453,266.0
3.5,0.05,0.0029187763037022796,0.13593539703903096,0.11966824644549763,743.0
4.0,0.05,0.0006703462313819897,0.041512535963830664,0.039857932123125495,2433.0
4.5,0.05,9.190850090968527e-05,0.006645611264640084,0.00660173867573044,15198.0
5.0,0.05,1.3433806155116967e-05,0.0010221740934530255,0.0010211303204933778,98809.0
5.5,0.05,1.5555555555555556e-06,0.000126,0.00012598412600012398,500000.0
1.0,0.15,0.33667295300958666,1.0,0.5,101.0
1.5,0.15,0.33075986170045574,1.0,0.5,101.0
2.0,0.15,0.32374666038032374,1.0,0.5,101.0
2.5,0.15,0.31655665566556657,1.0,0.5,101.0
3.0,0.15,0.30365000785792867,1.0,0.5,101.0
3.5,0.15,0.309013044161559,1.0,0.5,101.0
4.0,0.15,0.3084040546911834,1.0,0.5,101.0
4.5,0.15,0.3033160458903033,1.0,0.5,101.0
5.0,0.15,0.3023338048090523,1.0,0.5,101.0
5.5,0.15,0.30788982259570497,0.9901960784313726,0.4975369458128079,102.0
1 SNR gamma BER FER DFR num_iterations
2 1.0 0.01 0.09354864057834354 1.0 0.5 101.0
3 1.5 0.01 0.07331447430457332 1.0 0.5 101.0
4 2.0 0.01 0.05638063806380638 1.0 0.5 101.0
5 2.5 0.01 0.040782649693540785 1.0 0.5 101.0
6 3.0 0.01 0.024859943977591035 0.9901960784313726 0.4975369458128079 102.0
7 3.5 0.01 0.01549865229110512 0.9528301886792453 0.48792270531400966 106.0
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21 5.5 0.05 1.5555555555555556e-06 0.000126 0.00012598412600012398 500000.0
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26 3.0 0.15 0.30365000785792867 1.0 0.5 101.0
27 3.5 0.15 0.309013044161559 1.0 0.5 101.0
28 4.0 0.15 0.3084040546911834 1.0 0.5 101.0
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31 5.5 0.15 0.30788982259570497 0.9901960784313726 0.4975369458128079 102.0

9
latex/thesis/res/hybrid/2d_ber_fer_dfr_pegreg252x504_metadata.json Normal file
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@ -0,0 +1,9 @@
{
"duration": 3169.7098331579764,
"name": "2d_BER_FER_DFR_pegreg252x504",
"platform": "Linux-6.1.6-arch1-3-x86_64-with-glibc2.36",
"omega": 0.05,
"K": 200,
"min_var_k": 150,
"end_time": "2023-01-24 14:58:01.240346"
}

8
latex/thesis/res/hybrid/fps_vs_n.csv Normal file
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@ -0,0 +1,8 @@
n,k,fps,spf
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204,102,6601.111655956669,0.00015148963570365097
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408,204,317.62940489539665,0.0031483231230727054
31,11,8433.078242796635,0.00011858066191359955
31,26,61715.460243456524,1.6203395325177478e-05
504,252,195.7683929010524,0.0051080768717626035
1 n k fps spf
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3 204 102 6601.111655956669 0.00015148963570365097
4 204 102 1450.823819165217 0.000689263566526903
5 408 204 317.62940489539665 0.0031483231230727054
6 31 11 8433.078242796635 0.00011858066191359955
7 31 26 61715.460243456524 1.6203395325177478e-05
8 504 252 195.7683929010524 0.0051080768717626035

205
latex/thesis/res/proximal/extreme_components_20433484_variance.csv Normal file
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@ -0,0 +1,205 @@
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202 200 1.1137919258655136 0.0
203 201 0.34364650124488877 0.0
204 202 0.8982288426167987 0.0
205 203 0.7158776862928066 0.0

8
latex/thesis/res/proximal/fps_vs_n.csv Normal file
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n,k,fps,spf
96,48,23963.664002681122,4.1729845648316434e-05
204,102,11466.593636251799,8.720985775919413e-05
204,102,1262.3084456970446,0.0007921994053108008
408,204,291.5566845813344,0.0034298647669010448
31,11,48018.582682609645,2.0825271054119614e-05
31,26,72986.7772585266,1.3701111866576847e-05
504,252,252.54094111529753,0.0039597539930899765
1 n k fps spf
2 96 48 23963.664002681122 4.1729845648316434e-05
3 204 102 11466.593636251799 8.720985775919413e-05
4 204 102 1262.3084456970446 0.0007921994053108008
5 408 204 291.5566845813344 0.0034298647669010448
6 31 11 48018.582682609645 2.0825271054119614e-05
7 31 26 72986.7772585266 1.3701111866576847e-05
8 504 252 252.54094111529753 0.0039597539930899765