Added paragraph to discussion

latex/thesis/abbreviations.tex

@@ -70,6 +70,11 @@
     long  = maximum likelihood
 }
 
+\DeclareAcronym{MIMO} {
+    short = MIMO,
+    long  = multiple-input multiple-output
+}
+
 %
 % I
 %

latex/thesis/chapters/discussion.tex

@@ -1,12 +1,15 @@
 \chapter{Discussion}%
 \label{chapter:discussion}
 
-While the modified proximal decoding algorithm presented in section
+A modification of the implementation to reduce the memory requirements, even
-\ref{sec:prox:Improved Implementation} shows some promising results, further
+at some cost with regard to the running time, would allow for the examination
-investigation is required to determine how different choices of parameters
+of longer codes.
-affect the decoding performance.
+This in turn would make possible studying the behavior of the decoding
-Additionally, a more mathematically rigorous foundation for determining the
+algorithms covered here in error-rate regions where traditional approaches
-potentially wrong components of the estimate is desirable.
+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.