Abstract
In this chapter we consider the problem of safe transmission of a message over a channel, which cannot be affected by noise. We are looking for error-free and fastest possible methods for transmitting messages. This is a rather special, but important, problem in classical information theory. We rely mainly on the following two central tools: prefix-free sets and Shannon entropy. Undoubtedly, the prefix-free sets are the easiest codes to construct, and most interesting problems on codes can be raised for prefix-free sets. Shannon entropy is a measure of the degree of ignorance concerning which possibility holds in an ensemble with a given a priori probability distribution. Later on, we shall contrast the Shannon measure with the information content of an individual (finite) object — viewed as a measure of how difficult it is to specify that object.
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© 1994 Springer-Verlag Berlin Heidelberg
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Calude, C. (1994). Noiseless Coding. In: Information and Randomness. Monographs in Theoretical Computer Science An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03049-3_2
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DOI: https://doi.org/10.1007/978-3-662-03049-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03051-6
Online ISBN: 978-3-662-03049-3
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