Abstract
Compression of files is an important practical question. Memory is always a limiting resource so if our files can be stored in a more economic fashion, this has to be done. Some files, like pictures, contain a lot of redundancy and can be compressed significantly even without loss of quality of pictures. Here we give a glimpse of the combinatorial approach to the problem describing Fitingof’s compression codes. These codes are universal as they can be used when we do not know how the data was generated. Fitingof’s codes have an elegant decoding procedure using the Pascal triangle.
Good things, when short, are twice as good.
Baltasar Gracián y Morales (1601–1658)
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Notes
- 1.
In this chapter we will identify vectors from \(\mathbb Z_{2}^{n}\) and words of length n in the binary alphabet.
References
Kolmogorov, A.N.: Three approaches to the definition of the concept “the quantity of information”. Probl. Inf. Transm. 1(1), 3–11 (1965)
Fitingof, B.M.: Optimal encoding under an unknown or changing statistics. Probl. Inf. Transm. 2(2), 3–11 (1966)
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© 2015 Springer International Publishing Switzerland
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Slinko, A. (2015). Compression. In: Algebra for Applications. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-21951-6_8
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DOI: https://doi.org/10.1007/978-3-319-21951-6_8
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