Maximal Codeword Lengths in Huffman Codes
نویسنده
چکیده
In this article, the authors consider the following question about Huffman coding, which is an important technique for compressing data from a discrete source. If p is the smallest source probability, how long, in terms of p, can the longest Huffman codeword be? It is shown that if p is in the range 0 < p _< I/2, and if K is the unique index such that I/FI<+3 < p _< 1/FK+2, where FK denotes the Kth Fibonacci number, then the Iongest tluffman codeword for a source whose least probability is p is at most K, and no better bound is possible. Asymptotically, this implies the surprising fact that for small values of p, a Huffman code's longest codeword can be as much as 44 percent larger than that of the corresponding Shannon code.
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