On Optimal Weighted Binary Trees

Abstract

A new recursive top-down algorithm for the construction of a unique Huffman tree is introduced. We show that the prefix codes generated from the Huffman tree are unique and the weighted path length is optimal. Initially we have not imposed any restriction on the maximum length (the number of bits) a prefix code can take. But if buffering of the source is required, we have to put a restriction on the length of the prefix code. In this context we extend the top-down recursive algorithm for generating length-limited prefix codes.