A Comparative Analysis of Huffman Coding with Uniform Coding

In this paper, we analyze the compression ratio achieved by Huffman coding with that of uniform coding. For this, we first study the skewness property of the Huffman coding tree. We demonstrate that this tree will be completely skewed when the sorted frequency distribution of characters satisfies certain prefix properties. We also establish that among all the frequency distributions f1, f2, …, fn of a set of n characters that satisfy the prefix property, the average code length is maximum when the frequency distribution is a Fibonacci sequence. Then we estimate the average code length of Huffman coding for this frequency distribution.