Optimal coding

  • Alexander Shen
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)


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).


Binary String Code Length Code Word Optimal Code Huffman Code 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Laboratoire d’Informatique Fondamentale de Marseille (LIF) CNRSUniversité de la Méditerranée, Université de ProvenceMarseille Cedex 13France
  2. 2.Russian Academy of SciencesInstitute for Information Transmission ProblemsMoscowRussia

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