begin compression

compression.tex

@@ -1,2 +1,61 @@
+\documentclass{article}
+\usepackage[utf8x]{inputenc}
+\usepackage[margin=1in]{geometry} % Adjust margins
+\usepackage{caption}
+\usepackage{wrapfig}
+\usepackage{subcaption}
+\usepackage{parskip} % dont indent after paragraphs, figures
+\usepackage{xcolor}
+%\usepackage{csquotes} % Recommended for biblatex
+\usepackage{tikz}
+\usepackage{pgfplots}
+\usetikzlibrary{positioning}
+%\usegdlibrary{trees}
+\usepackage{float}
+\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{compression.bib}
 
-Compression codes (theorems: Kraft, Shannon-Fano, Huffman, arithmetic and LZW code)
+
+
+
+\title{Compression}
+\author{Erik Neller}
+\date{\today}
+
+\begin{document}
+\maketitle
+\section{Introduction}
+As the volume of data grows exponentially around the world, compression is only gaining in importance to all disciplines.
+Not only does it enable the storage of large amounts of information needed for research in scientific domains
+like DNA sequencing and analysis, it also plays a vital role in keeping stored data accessible by
+facilitating cataloging, search and retrieval.
+The concept of entropy is closely related to the design of efficient codes.
+
+\begin{equation}
+    H = E(I) = - \sum_i p_i \log_2(p_i)
+    \label{eq:entropy-information}
+\end{equation}
+The understanding of entropy as the expected information $E(I)$ of a message provides an intuition that,
+given a source with a given entropy (in bits), any coding can not have a lower average word length (in bits)
+than this entropy without losing information.
+This is the content of Shannons's source coding theorem \cite{enwiki:shannon-source-coding}.
+
+
+% https://en.wikipedia.org/wiki/Shannon%27s_source_coding_theorem
+\section{Kraft-McMillan inequality}
+% https://de.wikipedia.org/wiki/Kraft-Ungleichung
+% https://en.wikipedia.org/wiki/Kraft%E2%80%93McMillan_inequality
+\section{Shannon-Fano}
+% https://de.wikipedia.org/wiki/Shannon-Fano-Kodierung
+\section{Huffman Coding}
+% https://de.wikipedia.org/wiki/Huffman-Kodierung
+\section{LZW Algorithm}
+% https://de.wikipedia.org/wiki/Lempel-Ziv-Welch-Algorithmus
+\section{Arithmetic Coding}
+% https://en.wikipedia.org/wiki/Arithmetic_coding
+
+\printbibliography
+\end{document}