Fixed-rate encoding of individual sequences with side information

For every infinite sequence and a given side-information sequence , we define a quality called the finite-state conditional complexity of given . It is shown that is the smallest asymptotically attainable fixed-rate at which can be transmitted with negligibly small distortion, given . Moreover, it is demonstrated that in order to achieve an arbitrary small distortion for all sequences such that is less than the allowable transmission rate it is not necessary for the encoder to have access to the side-information sequence (provided it is available to the decoder). This result is a generalization of the classical Slepian-Wolf result for cases where the probabilistic characterization of and is not known, or does not exist.