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