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Removed invalid reference from comparison chapter

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Andreas Tsouchlos 2023-04-11 18:11:26 +02:00
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latex/thesis/chapters/comparison.tex
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@ -113,15 +113,13 @@ time, with \ac{ADMM} each parity check is
considered separately and 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 \ref{subsec:prox:conv_properties}), this is not the oscillatory behaviour (as explained in section
case with \ac{ADMM}, which partly explains the disparate decoding performance \ref{subsec:prox:conv_properties}), this is not the case with \ac{ADMM}, which
of the two methods. partly explains the disparate decoding performance of the two methods.
Furthermore, while with proximal decoding the step considering the constraints Furthermore, while with proximal decoding the step considering the constraints
is realized using gradient descent - amounting to an approximation - is realized using gradient descent - amounting to an approximation -
with \ac{ADMM} it reduces to a number of projections onto the parity polytopes with \ac{ADMM} it reduces to a number of projections onto the parity polytopes
$\mathcal{P}_{d_j}$ (see $\mathcal{P}_{d_j}$ which always provide exact results.
\ref{chapter:LD Decoding using ADMM as a Proximal Algorithm}),
which always provide exact results.
The contrasting treatment of the constraints (global and approximate with The contrasting treatment of the constraints (global and approximate with
proximal decoding, local and exact with \ac{ADMM}) also leads to different proximal decoding, local and exact with \ac{ADMM}) also leads to different