Mathematics of Data Compression

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Data Compression I. Introduction In the modern era known as the “Information Age,” forms of electronic information are steadily becoming more important. Unfortunately, maintenance of data requires valuable resources in storage and transmission, as even the presence of information in storage re-quires some power. However, some of the largest files are those that are in formats re-plete with repetition, and thus are larger than they need to be. The study of data compres-sion is the science which attempts to advance toward methods that can be applied to data in order to make it take up less space. The uses for this are vast, and algorithms will need to be improved in order to sustain the inevitably larger files of the future. Thus, I decided to focus my research on the techniques that successful methods use in order to save space. My research question: What common features do good methods of data compression share? II. Mathematical Context The history of data compression is not so much a continent of improvement as it is an archipelago of dispersed -but related- innovations in the subject of information theory. The reason for this is mostly its relatively new development. Many topics in mathematics are now mostly researched in terms of computing. However, most of these subjects were already fairly developed before the arrival of computers. Cryptography, for example, was used since ancient times to keep information secret, and has only now developed into methods that assume the use of a computer. In contrast, computers are almost a require-ment for data compression as a theory to be of practical utilization: Analog information can easily be compressed by recording it in less space. Anyhow, there is rarely a need to store info... ... middle of paper ... ...hm).” “LZW.” „Minimum description length.” “Run-length Encoding.” “Shannon-Fano coding.” “Wikipedia:Citing Wikipedia” "Historical Notes: History [of data compression]." [Excerpt from book; A New Kind of Science, by Stephen Wolfram] ©2002 Stephen Wolfram. Wolfram Science. 31 July 2005 . Lynch, Thomas D. Data Compression: Techniques and Applications. Belmont, California, Lifetime Learning Productions. ©1985 Solomon, David. Data Compression: The Complete Reference. New York, Springer Verlag. ©1998 Appendix B: Mathematica Code for BLM 8

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