Bounds on the redundancy of binary alphabetical codes

An alphabetical code is a code in which the numerical binary order of the codewords corresponds to the alphabetical order of the encoded symbols. A necessary and sufficient condition for the existence of a binary alphabetical code is presented. The redundancy of the optimum binary alphabetical code is given in comparison with the Huffman code and its upper bound, which is tighter than bounds previously reported, is presented. The redundancy of the optimal alphabetical code is about 5% in comparison with the Huffman coding, which shows the usefulness of the alphabetical code. >