Asymptotic average redundancy of Huffman (and Shannon-Fano) block codes

Abstract

A Huffman code is an iterative algorithm built over the associated Huffman tree, in which the two nodes with lowest weights are combined into a new node with a weight that is the sum of the weights of its two children. Such a construction is not unique but fortunately with a simple modification to the Huffman algorithm, it is possible to construct a unique Huffman code so that the longest codewords are as short as possible. Here we deal with such modified Huffman codes and present precise asymptotic results on the average redundancy of such codes for memoryless sources.