This paper presents some tighter bounds on universal noiseless coding, in particular, the lowerbound tighter than Davisson et al.'s for finite sequence and the upperbound for some typical universal data compression. We find that Davisson et al.'s bound satisfies some optimization in the case of using the Jeffreys prior and also that the derived upperbound in this paper is within O(1/n) from the Clarke and Barron asymptotics in the case of some restricted typical universal data compression defined in the paper.

This paper's main objective is to clearly describe the construction of a universal code for minimizing Davisson's minimax redundancy in a range where the true model and stochastic parameters are unknown. Minimax redundancy is defined as the maximum difference between the expected persymbol code length and the per-symbol source entropy in the source range. A universal coding scheme is here formulated in terms of the weight function, i.e., a method is presented for determining a weight function which minimizes the minimax redundancy even when the true model is unknown. It is subsequently shown that the minimax redundancy achieved through the presented coding method is upper-bounded by the minimax redundancy of Rissanen's semi-predictive coding method.