An extension of asymptotically sufficient statistic method for pointwise strong universality

In the previous work in Proc. ISIT2003 and Proc. ISITA2004, we have investigated some relationships between sufficient statistic and weakly universal lossless source coding, and proposed asymptotically sufficient statistic method to evaluate the pointwise redundancy of source codes. This method is an attempt to understand the universality of general lossless source codes from a simple and unified viewpoint. In this paper, we present a new theorem which enables our method to show the pointwise strong universality of lossless source codes. As an example of the theorem, we prove the pointwise strong universality of the original Lynch-Davisson code and conditional Lynch-Davisson code for the class of stationary memoryless and Markov sources, respectively. Moreover, it is shown that this method can be applied to the class of finite state sources. We prove that a blockwise Lynch-Davisson code is pointwise strongly universal for this class. From the viewpoint of our method, all of these algorithms can be seen as examples of a two-step source code using a kind of asymptotically sufficient statistic. The result of this paper gives a unified viewpoint for the universality of context-based algorithms and block-based algorithms, which are typical two types of universal lossless source coding algorithms