Sequential prediction and ranking in universal context modeling and data compression

We investigate the use of prediction as a means of reducing the model cost in lossless data compression. We provide a formal justification to the combination of this widely accepted tool with a universal code based on context modeling, by showing that a combined scheme may result in faster convergence rate to the source entropy. In deriving the main result, we develop the concept of sequential ranking, which can be seen as a generalization of sequential prediction, and we study its combinatorial and probabilistic properties.