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