2008 Volume E91.A Issue 3 Pages 836-845
This paper investigates the fixed-slope lossy coding of individual sequences and nonstationary sources. We clarify that, for a given individual sequence, the optimal cost attainable by the blockwise lossy encoders is equal to the optimal average cost with respect to the empirical distribution of the given sequence. Moreover, we show that, for a given nonstationary source, the optimal cost attainable by the blockwise encoders is equal to the supremum of the optimal average cost over all the stationary sources in the stationary hull of the given source. In addition, we show that the universal lossy coding algorithm based on Lempel-Ziv 78 code attains the optimal cost for any individual sequence and any nonstationary source.
