Enhanced static Fano coding

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. Canonical codes, in which the code words are arranged in a lexicographical order, are advantageous because they can be decoded extremely expediently. Although Huffman\´s algorithm is optimal, the generation of a canonical Huffman code is not straightforward. Conversely, while the Fano coding is sub-optimal, it can lead to canonical codes. In this paper, we resolve the dilemma by focusing on the static implementation of Fano\´s method. 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 Fanol by presenting some properties of Fano trees, and the theory of list rearrangements. Our enhanced algorithm achieves compression ratios arbitrarily close to those of Huffman\´s algorithm. Empirical results on files of the Canterbury corpus corroborate the almost-optimal efficiency of our enhanced algorithm and its canonical nature. We believe that the compression efficiency of Fano+ can be made to attain the compression ratios of the best known schemes if a structure model of the data is also incorporated