entropy sources

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}