Optimization of transition diagram weights for sequential lossless coding of piecewise stationary sources

The second order terms of the redundancy of an asymptotically optimal, transition diagram based, universal sequential lossless coding scheme for sources with abruptly changing statistics can be further reduced by correctly choosing the transition weights in the diagram. Such optimal transition weights are presented for cases that differ in the amount of prior knowledge one has on the time elapsing between two consecutive changes in the statistics. Particularly, an optimal choice of weights is proposed for the most extreme case, where no such prior knowledge exists at all.