A nearly-optimal Fano-based coding algorithm

Statistical coding techniques have been used for a long time in lossless data compression, using methods such as Huffman's algorithm, arithmetic coding, Shannon's method, Fano's method, etc. Most of these methods can be implemented either statically or adaptively. In this paper, we show that although Fano coding is sub-optimal, it is possible to generate static Fano-based encoding schemes which are arbitrarily close to the optimal, i.e. those generated by Huffman's algorithm. By taking advantage of the properties of the encoding schemes generated by this method, and the concept of "code word arrangement", we present an enhanced version of the static Fano's method, namely Fano+. We formally analyze Fano+ by presenting some properties of the Fano tree, and the theory of list rearrangements. Our enhanced algorithm achieves compression ratios arbitrarily close to those of Huffman's algorithm on files of the Calgary corpus and the Canterbury corpus