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\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

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\end{document}