Abstract
In this chapter we consider basic notions of coding theory. After introducing the notions of prefix and uniquely decodable codes (section 12.1) we prove the classical Kraft–McMillan inequality, a necessary and sufficient condition for the existence of a uniquely decodable code with given lengths of code words (section 12.2). Then (section 12.3) we discuss an algorithm that allows us to find an optimal uniquely decodable code for given letter frequencies. Finally, we discuss lower and upper bounds for the effectiveness of the optimal code (section 12.4).
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© 2010 Springer Science+Business Media, LLC
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Shen, A. (2010). Optimal coding. In: Algorithms and Programming. Springer Undergraduate Texts in Mathematics and Technology. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1748-5_12
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DOI: https://doi.org/10.1007/978-1-4419-1748-5_12
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1747-8
Online ISBN: 978-1-4419-1748-5
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