We establish a coding theorem and a matching converse theorem for separate encodings and joint decoding of individual sequences using finite-state machines. The achievable rate region is characterized in terms of the Lempel-Ziv (LZ) complexities, the conditional LZ complexities and the joint LZ complexity of the two source sequences. An important feature that is needed to this end, which may be interesting on its own right, is a certain asymptotic form of a chain rule for LZ complexities, which we establish in this work. The main emphasis in the achievability scheme is on the universal decoder and its properties. We then show that the achievable rate region is universally attainable by a modified version of Draper's universal incremental Slepian-Wolf (SW) coding scheme, provided that there exists a low-rate reliable feedback link.

26 pages; submitted for publication