On the Data Expansion of the Huffman Compression Algorithm

While compressing a file with a Huffman code, it is possible that the size of the file grows temporarily. This happens when the source letters with low frequencies (to which long codewords are assigned) are encoded first. The maximum data expansion is the average growth in bits per source letter resulting from the encoding of a source letter with a long codeword. It is a measure of the worst case temporary growth of the file. In this paper we study the maximum data expansion of Huffman codes. We provide some new properties of the maximum data expansion δ of Huffman codes and using these properties we prove that δ < 1.256.