Optimal maximal and maximal prefix codes equivalent to Huffman codes

Novel maximal coding and maximal prefix coding are introduced. We show that for finite source alphabets all Huffman codes are optimal maximal codes and optimal maximal prefix codes. Conversely, optimal maximal codes or optimal maximal prefix codes need not to be Huffman codes. For any maximal prefix code C, however, there exists some information source I such that C is exactly a Huffman code for I. And, for any maximal code C, there exists some information source I such that C is equivalent to a Huffman code for I. In other words, the class of Huffman codes coincides with the one of maximal prefix codes or maximal codes. Additionally, a case study of data compression is investigated. The optimal maximal coding and maximal prefix coding are used not only for statistical modeling but also for dictionary methods. Finally, it is proven that given an original file and a corresponding encoded file by the maximal prefix coding, the complexity of guessing the maximal prefix code is NP-complete.