From b9d2227b024bd36e1cd730b5832c6b5825e73302 Mon Sep 17 00:00:00 2001 From: Andreas Tsouchlos Date: Tue, 11 Apr 2023 18:11:26 +0200 Subject: [PATCH] Removed invalid reference from comparison chapter --- latex/thesis/chapters/comparison.tex | 10 ++++------ 1 file changed, 4 insertions(+), 6 deletions(-) diff --git a/latex/thesis/chapters/comparison.tex b/latex/thesis/chapters/comparison.tex index eaedd88..f4474cc 100644 --- a/latex/thesis/chapters/comparison.tex +++ b/latex/thesis/chapters/comparison.tex @@ -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). This difference means that while with proximal decoding the alternating 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 -case with \ac{ADMM}, which partly explains the disparate decoding performance -of the two methods. +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 of the two methods. Furthermore, while with proximal decoding the step considering the constraints is realized using gradient descent - amounting to an approximation - with \ac{ADMM} it reduces to a number of projections onto the parity polytopes -$\mathcal{P}_{d_j}$ (see -\ref{chapter:LD Decoding using ADMM as a Proximal Algorithm}), -which always provide exact results. +$\mathcal{P}_{d_j}$ which always provide exact results. The contrasting treatment of the constraints (global and approximate with proximal decoding, local and exact with \ac{ADMM}) also leads to different