On Antiuniform And Partially Antiuniform Sources

A source S = {s₁, s₂, ...} having a binary Huffman code with codeword lengths satisfying l₁ = 1, l₂ = 2, ...(and l_n-1 = ln = n - 1 when |S| = n) is called an antiuniform source. If l₁ = 1, l₂ = 2, ..., li = i, then the source is called an i-level partially antiuniform source. In this paper the redundancy, the expected codeword lengths, and the entropy of partially antiuniform sources is studied. It is shown that the range of the redundancy R of a given i-level partially antiuniform source with distribution {pi} is an interval of length pi+1 + ... +pn. This results in a realistic approximation for R. An upper bound is derived for the expected codeword lengths L of antiuniform sources. It is shown that L is less than three. The entropy H of any antiuniform source with average codeword lengths L is bounded above by LlogL - (L - 1) log(L - 1) and hence it does not exceed 2.76.