entropy sources

entropy.bib

@@ -0,0 +1,35 @@
+  @misc{ enwiki:shannon-hartley,
+    author = "{Wikipedia contributors}",
+    title = "Shannon–Hartley theorem --- {Wikipedia}{,} The Free Encyclopedia",
+    year = "2025",
+    howpublished = "\url{https://en.wikipedia.org/w/index.php?title=Shannon%E2%80%93Hartley_theorem&oldid=1316080633}",
+    note = "[Online; accessed 29-October-2025]"
+  }
+  @misc{ enwiki:noisy-channel,
+    author = "{Wikipedia contributors}",
+    title = "Noisy-channel coding theorem --- {Wikipedia}{,} The Free Encyclopedia",
+    year = "2025",
+    howpublished = "\url{https://en.wikipedia.org/w/index.php?title=Noisy-channel_coding_theorem&oldid=1285893870}",
+    note = "[Online; accessed 29-October-2025]"
+  }
+  @misc{ enwiki:source-coding,
+    author = "{Wikipedia contributors}",
+    title = "Shannon's source coding theorem --- {Wikipedia}{,} The Free Encyclopedia",
+    year = "2025",
+    howpublished = "\url{https://en.wikipedia.org/w/index.php?title=Shannon%27s_source_coding_theorem&oldid=1301398440}",
+    note = "[Online; accessed 29-October-2025]"
+  }
+ @misc{ dewiki:nyquist-shannon,
+   author = "Wikipedia",
+   title = "Nyquist-Shannon-Abtasttheorem --- Wikipedia{,} die freie Enzyklopädie",
+   year = "2025",
+   url = "\url{https://de.wikipedia.org/w/index.php?title=Nyquist-Shannon-Abtasttheorem&oldid=255540066}",
+   note = "[Online; Stand 29. Oktober 2025]"
+ }
+  @misc{ enwiki:information-content,
+    author = "{Wikipedia contributors}",
+    title = "Information content --- {Wikipedia}{,} The Free Encyclopedia",
+    year = "2025",
+    howpublished = "\url{https://en.wikipedia.org/w/index.php?title=Information_content&oldid=1313862600}",
+    note = "[Online; accessed 29-October-2025]"
+  }

entropy.tex

@@ -10,6 +10,8 @@
 \usepackage{amsmath}
 \PassOptionsToPackage{hyphens}{url}
 \usepackage{hyperref} % allows urls to follow line breaks of text
+\usepackage[style=ieee, backend=biber, maxnames=1, minnames=1]{biblatex}
+\addbibresource{entropy.bib}
 
 
 
@@ -147,7 +149,10 @@ as a cost function in machine learning
 % relation to hamming distance and efficient codes
 
 \subsection{Noisy communication channels}
-Given a model of 
+The noisy channel coding theorem was stated by \textit{Claude Shannon} in 1948, but first rigorous proof was
+provided in 1954 by Amiel Feinstein.
+It is of foundational to information theory, stating that given a noisy channel with capacity $C$
+and information transmitted at $R$ \cite{enwiki:shannon-hartley}
 
 \begin{figure}[H]
 \begin{tikzpicture}
@@ -173,4 +178,31 @@ Given a model of
 \label{fig:noisy-channel}
 \end{figure}
 
+\begin{figure}[H]
+\begin{tikzpicture}
+    \def\boxw{2.5cm}
+    \def\n{4}
+    \pgfmathsetmacro{\gap}{(\textwidth - \n*\boxw)/(\n-1)}
+    \node (S) at (0,0) [draw, align=center, text width=\boxw] {Information Source};
+    \node (S0) at (\boxw + \gap,1) [draw, circle] {0};
+    \node (S1) at (\boxw + \gap,-1) [draw, circle] {1};
+    \node (D0) at ({2*(\boxw + \gap)},1) [draw, circle] {0};
+    \node (D1) at ({2*(\boxw + \gap)},-1) [draw, circle] {1};
+    \node (D) at ({3*(\boxw + \gap)},0) [draw, align=center, text width=\boxw] {Destination};
+
+    \draw[->] (S) -- (S0);
+    \draw[->] (S) -- (S1);
+
+    \draw[->,dashed] (S0) -- (D0) node[midway, above] {$p$};
+    \draw[->,dashed] (S0) -- (D1) node[pos=0.8, above] {$1-p$};
+    \draw[->,dashed] (S1) -- (D0) node[pos= 0.2, above] {$1-p$};
+    \draw[->,dashed] (S1) -- (D1) node[midway, below] {$p$};
+
+    \draw[->] (D0) -- (D);
+    \draw[->] (D1) -- (D);
+\end{tikzpicture}
+\caption{Model of a binary symmetric channel}
+\label{fig:binary-channel}
+\end{figure}
+
 \end{document}