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Paper IPM / M / 8498  


Abstract:  
A source S = {S_{1}, S_{2},...} having a binary Huffman code with
codeword lengths satisfying l_{1} = 1, l_{2} = 2, ... is called an
antiuniform source. If l_{1} = 1, l_{2} = 2, ... , l_{i} = i, then the
source is called an ilevel partially antiuniform source. This
paper deals with the redundancy, expected codeword length and
entropy of antiuniform sources. A tight upper bound is derived for
the expected codeword length L of antiuniform sources. It is
shown that L does not exceed [(√5+3)/2]. For each 1 < L ≤ [(√5+3)/2] we introduce an antiuniform
distribution achieving maximum entropy H(P)max =
LlogL(Ll)log(Ll). This shows that the maximum entropy achieved
by antiuniform distributions does not exceed 2.512. It is shown
that the range of redundancy values for ilevel partially
antiuniform sources with distribution {Pi} is an interval of
length ∑_{j=i+1}Pj. This results in a realistic approximation
for the redundancy of these sources.
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