diff --git a/latex/thesis/chapters/decoding_techniques.tex b/latex/thesis/chapters/decoding_techniques.tex
index 7014eeb..cfc4788 100644
--- a/latex/thesis/chapters/decoding_techniques.tex
+++ b/latex/thesis/chapters/decoding_techniques.tex
@@ -578,7 +578,7 @@ The resulting formulation of the relaxed optimization problem is the following:%
     \end{subfigure}
     
     \caption{Visualization of the codeword polytope and the relaxed codeword
-    polytope for an example code}
+    polytope}
     \label{fig:dec:poly}
 \end{figure}%
 %
@@ -651,7 +651,7 @@ the so-called \textit{code-constraint polynomial} is introduced:%
 .\end{align*}%
 %
 The intention of this function is to provide a way to penalize vectors far
-from a codeword and favor those close to a codeword.
+from a codeword and favor those close to one.
 In order to achieve this, the polynomial is composed of two parts: one term
 representing the bipolar constraint, providing for a discrete solution of the
 continuous optimization problem, and one term representing the parity
@@ -781,7 +781,7 @@ it suffices to consider only proportionality instead of equality.}%
     &\propto \boldsymbol{x} - \boldsymbol{y}
 ,\end{align*}%
 %
-Allowing equation \ref{eq:prox:step_log_likelihood} to be rewritten as%
+allowing equation \ref{eq:prox:step_log_likelihood} to be rewritten as%
 %
 \begin{align*}
     \boldsymbol{r} \leftarrow \boldsymbol{s}
@@ -823,6 +823,6 @@ return $\boldsymbol{\hat{c}}$
     \end{genericAlgorithm}
 
 
-    \caption{Proximal decoding algorithm}
+    \caption{Proximal decoding algorithm for an \ac{AWGN} channel}
     \label{fig:prox:alg}
 \end{figure}