Conditional Lempel-Ziv complexity and its application to source coding theorem with side information

This paper proposes the conditional LZ complexity and analyzes its property. Especially, we show an inequality corresponding to Ziv´s inequality concerning a distinct parsing of a pair of sequences. Further, as a byproduct of the result, we show a simple proof of the asymptotical optimality of Ziv´s universal source coding algorithm with side information.