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Added reference and TODO

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Andreas Tsouchlos 2023-04-10 11:48:28 +02:00
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latex/thesis/chapters/comparison.tex
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@ -110,10 +110,10 @@ subjected to.
Their major differece is that while with proximal decoding the constraints Their major differece is that while with proximal decoding the constraints
are regarded in a global context, considering all parity checks at the same are regarded in a global context, considering all parity checks at the same
time, with \ac{ADMM} each parity check is time, with \ac{ADMM} each parity check is
considered separately, in a more local context (line 4 in both algorithms). considered separately and in a more local context (line 4 in both algorithms).
This difference means that while with proximal decoding the alternating This difference means that while with proximal decoding the alternating
minimization of the two parts of the objective function inevitably leads to minimization of the two parts of the objective function inevitably leads to
oscillatory behaviour (as explained in section (TODO)), this is not the oscillatory behaviour (as explained in section \ref{subsec:prox:conv_properties}), this is not the
case with \ac{ADMM}, which partly explains the disparate decoding performance case with \ac{ADMM}, which partly explains the disparate decoding performance
of the two methods. of the two methods.
Furthermore, while with proximal decoding the step considering the constraints Furthermore, while with proximal decoding the step considering the constraints
@ -133,6 +133,8 @@ itself.
The advantage which arises because of this when using \ac{ADMM} is that The advantage which arises because of this when using \ac{ADMM} is that
it can be easily detected, when the algorithm gets stuck - the algorithm it can be easily detected, when the algorithm gets stuck - the algorithm
returns a pseudocodeword, the components of which are fractional. returns a pseudocodeword, the components of which are fractional.
\todo{Additional constraints can then be successively added, until a valid
codeword is returned}
\todo{Compare time complexity using Big-O notation} \todo{Compare time complexity using Big-O notation}
@ -149,7 +151,7 @@ returns a pseudocodeword, the components of which are fractional.
\item \ac{ADMM} faster than proximal decoding $\rightarrow$ \item \ac{ADMM} faster than proximal decoding $\rightarrow$
Parallelism Parallelism
\item Proximal decoding faster than \ac{ADMM} $\rightarrow$ dafuq \item Proximal decoding faster than \ac{ADMM} $\rightarrow$ dafuq
(larger number of iterations before convergence?) (larger number of iterations before convergence? More values to compute for ADMM?)
\end{itemize} \end{itemize}