“School of Mathematics”
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| Paper IPM / M / 8498 |
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| Abstract: | |
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A source S = {S1, S2,...} having a binary Huffman code with
code-word lengths satisfying l1 = 1, l2 = 2, ... is called an
antiuniform source. If l1 = 1, l2 = 2, ... , li = i, then the
source is called an i-level 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-(L-l)log(L-l). 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 i-level partially
antiuniform sources with distribution {Pi} is an interval of
length ∑j=i+1Pj. This results in a realistic approximation
for the redundancy of these sources.
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