diff --git a/latex/thesis/abbreviations.tex b/latex/thesis/abbreviations.tex index 01365ca..7040fd3 100644 --- a/latex/thesis/abbreviations.tex +++ b/latex/thesis/abbreviations.tex @@ -70,6 +70,11 @@ long = maximum likelihood } +\DeclareAcronym{MIMO} { + short = MIMO, + long = multiple-input multiple-output +} + % % I % diff --git a/latex/thesis/chapters/discussion.tex b/latex/thesis/chapters/discussion.tex index 7506f19..26d2c20 100644 --- a/latex/thesis/chapters/discussion.tex +++ b/latex/thesis/chapters/discussion.tex @@ -1,12 +1,15 @@ \chapter{Discussion}% \label{chapter:discussion} - -While the modified proximal decoding algorithm presented in section -\ref{sec:prox:Improved Implementation} shows some promising results, further -investigation is required to determine how different choices of parameters -affect the decoding performance. -Additionally, a more mathematically rigorous foundation for determining the -potentially wrong components of the estimate is desirable. + +A modification of the implementation to reduce the memory requirements, even +at some cost with regard to the running time, would allow for the examination +of longer codes. +This in turn would make possible studying the behavior of the decoding +algorithms covered here in error-rate regions where traditional approaches +exhibit an error floor. +The decoding algorithms could then be assessed for use in very +high reliability applications, where traditional methods like \ac{BP} or the +min-sum-algorithm fall short. As mentioned in section \ref{subsec:prox:conv_properties}, the alternating minimization of the two gradients in the proximal decoding algorithm leads to @@ -23,6 +26,18 @@ constraints are never truly satisfied; not even after the minimization step dealing with the constraint part of the objective function. Despite this, an initial examination by Yanxia Lu in \cite[Sec. 4.2.4.]{yanxia_lu_thesis} shows only limited success. +It is also important to note that while in this thesis proximal decoding was +examined with respect to its performance in \ac{AWGN} channels, in +\cite{proximal_paper} it is presented as a method applicable to non-trivial +channel models such as \ac{LDPC}-coded massive \ac{MIMO} channels, perhaps +broadening its usefulness beyond what is shown here. + +While the modified proximal decoding algorithm presented in section +\ref{sec:prox:Improved Implementation} shows some promising results, further +investigation is required to determine how different choices of parameters +affect the decoding performance. +Additionally, a more mathematically rigorous foundation for determining the +potentially wrong components of the estimate is desirable. Another interesting approach might be the combination of proximal and \ac{LP} decoding.