A universal data-base for data compression

A database for data compression is universal if, in its construction no prior knowledge of the source distribution is assumed and is optimal if, when we encode the reference index of the database, its encoding rate achieves the optimal encoding rate for any given source: in the noiseless case the entropy rate and in the semifaithful case the rate-distortion function of the source. We construct a universal database for all stationary ergodic sources, and prove the optimality of the thus constructed database for a block-shift type reference and a single-shift type reference.