Encoding of markov sources with partial memoryless side information at the decoder

We consider the one helper source coding problem posed and investigated by Ahlswede, Körner, and Wyner for a class of information sources with memory. For this class of information sources we derive single letter characterization of inner and outer bounds of the admissible rate region. Our characterizations involve new auxiliary random variables. In particular, the auxiliary random variables in the inner bound work as generators of Markov processes in the proof of direct coding theorem.