A universal coding scheme based on minimizing minimax redundancy for sources with an unknown model

The author describes the construction of a universal code for minimizing L.D. 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 per-symbol code length and the per-symbol source entropy in the source range. A universal coding scheme is 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 J. Rissanen´s semi-predictive coding method