Optimal synchronous coding

Novel synchronous coding schemes are introduced and relationships between optimal synchronous codes and Huffman codes are discussed. Although the problem of existence of the optimal synchronous codes has not yet resolved, we show that any synchronous code can be considered as an optimal synchronous code for some information source alphabet. In other words, synchronous codes are almost optimal and, therefore, are regarded as near optimal with respect to average code word length. It is shown that there always exist optimal synchronous codes for the information source alphabets with a dyadic probability distribution. Comparing with the Huffman coding, the synchronous coding is used not only for statistical modeling but also for dictionary methods. It is also good at using in a large information retrieval system like the Huffman coding. Moreover, from the viewpoint of computational difficulty, it is proven that breaking a synchronous or an optimal synchronous code is NP-complete. E-mail: itjia@cityu.edu.hk This work was partially sponsored by City U Grants 7001355, 863 Program (Project No. 2002AA144060) and the National Natural Science Foundation of China (Project No. 60273062). E-mail: mli@ee.ecnu.edu.cn