Fixed-rate encoding of individual sequences with side information

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