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Data Compression

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Introduction   ::   Kraft   ::   Optimal Codes   ::   Bounds   ::   Huffman   ::   Coding

Kraft Inequality

In this section we develop an inequality on the lengths of the codewords that is necessary and sufficient for a code to be an instantaneous code.
\begin{theorem} (Kraft inequality) For any instantaneous code over an alphabet ... ...uality there exists an instantaneous code with these word lengths. \end{theorem}

\begin{proof} Consider a $D$-ary tree representing the codewords: the path down... ...,l_m$\ which satisfy the inequality, we can always construct a tree. \end{proof}

Copyright 2008, by the Contributing Authors. Cite/attribute Resource. admin. (2006, May 17). Data Compression. Retrieved September 08, 2008, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Information_Theory/lecture6_2.htm. This work is licensed under a Creative Commons License. Creative Commons License
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