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An InternationalJournal computers &
 

Summary: PERGAMON
An InternationalJournal
computers &
mathematics
with applications
Computers and Mathematics with Applications 39 (2000) 129-134
www.elsevier,nl/locate/camwa
Maximal Codeword Lengths
in Huffman Codes
Y. S. ABU-MOSTAFA AND R. J. MCELIECE
Department of Electrical Engineering, California Institute of Technology
MS 136-93, Pasadena, CA 91125, U.S.A.
In celebration of the 60th birthday of Solomon W. Golomb
Abstract--In this paper, we 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? We show that if p is
in the range 0 < p <_ 1/2, and if K is the unique index such that 1/F/+3 < p < 1/FK+2, where
FK denotes the K th Fibonacci number, then the longest Huffman 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

  

Source: Abu-Mostafa, Yaser S. - Department of Mechanical Engineering & Computer Science Department, California Institute of Technology

 

Collections: Computer Technologies and Information Sciences