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On the Optimal Coding

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Advances in Multimedia Information Processing — PCM 2001 (PCM 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2195))

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Abstract

Novel coding schemes are introduced and relationships between optimal codes and Huffman codes are discussed. It is shown that, for finite source alphabets, the Huffman coding is the optimal coding, and conversely the optimal coding needs not to be the Huffman coding. It is also proven that there always exists the optimal coding for infinite source alphabets.We show that for every random variable with a countable infinite set of outcomes and finite entropy there exists an optimal code constructed from optimal codes for truncated versions of the random variable. And the average code word lengths of any sequence of optimal codes for the truncated versions converge to that of the optimal code. Furthermore, a case study of data compression is given. Comparing with the Huffman coding, the optimal coding is a more flexible compression method used not only for statistical modeling but also for dictionary schemes.

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Author information

Authors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, 83 Tat Chee Avenue Kowloon, Hong Kong, PRC

    Dongyang Long & Weijia Jia

Authors
  1. Dongyang Long
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  2. Weijia Jia
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Editor information

Editors and Affiliations

  1. Microsoft Research China, 5/F Beijing Sigma Center 49 Zhichung Road, Haidian District, Beijing, 100080, China

    Heung-Yeung Shum

  2. Institute of Information Science, Academia Sinica, Taiwan

    Mark Liao

  3. Department of Electrical Engineering, Columbia University, New York, NY, 10027, USA

    Shih-Fu Chang

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© 2001 Springer-Verlag Berlin Heidelberg

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Long, D., Jia, W. (2001). On the Optimal Coding. In: Shum, HY., Liao, M., Chang, SF. (eds) Advances in Multimedia Information Processing — PCM 2001. PCM 2001. Lecture Notes in Computer Science, vol 2195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45453-5_13

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  • DOI: https://doi.org/10.1007/3-540-45453-5_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42680-6

  • Online ISBN: 978-3-540-45453-3

  • eBook Packages: Springer Book Archive

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