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.

翻译：本文针对使用有限状态机对单个序列进行独立编码与联合解码，建立了编码定理及匹配的逆定理。可达速率区域通过两个源序列的Lempel-Ziv（LZ）复杂度、条件LZ复杂度及联合LZ复杂度来刻画。为实现这一目标所需的一个重要特征（其本身可能具有独立研究价值）是LZ复杂度的某种渐近形式的链式法则，本文对此予以建立。可达性方案的核心在于通用解码器及其特性。进一步研究表明，若存在低速率可靠反馈链路，则通过改进的Draper通用增量Slepian-Wolf（SW）编码方案可普遍实现该可达速率区域。