A universal data compression with common side information

We consider the coding problem of a source X when the sender and the receiver has access to a common source Y which is correlated with X. This problem is closely related to that of coding correlated sources which were studied by Slepian and Wolf (1973) in the noiseless case, and also to that of the source coding with side information at the decoder studied by Wyner and Ziv (1976) in the semifaithful case. In those works, they studied mainly the case where respective encoders can only see respective source outputs to be encoded. However, we instead construct an asymptotically optimum fixed-to-variable length block universal code with common side information available to both encoder and decoder. This is the definite difference between the previous and our results. Furthermore, both in the noiseless and the semifaithful case, our encoder construction does not depend on the random coding argument, but provides a deterministic encoding algorithm.