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Paper   IPM / M / 8498
School of Mathematics
  Title:   On information theory parameters of infinite antiunifrom sources
  Author(s):  M . Esmaeili (Joint with A. Kahbod)
  Status:   Published
  Journal: IET Communications
  Vol.:  1
  Year:  2007
  Pages:   1039-1041
  Supported by:  IPM
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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