On the coding for correlated sources we extend the Slepian-Wolf (1973) data compression system (called the SW system) to define a new system (called the SWL system), where two separate encoders of the SW system are mutually linked. Determining the optimal error exponent for all rates inside the admissible rate region remains an open problem for the SW system. We completely solve this problem for the SWL system, and show that the optimal exponents can be achieved by universal codes. Furthermore, it is shown that the linkage of two encoders does not extend the admissible rate region and does not even improve the exponent of correct decoding outside this region. The zero error data transmission problem for the SWL system is also considered. We determine the zero error rate region, the admissible rate region under the condition that the decoding error probability is strictly zero, and show that this region can be attained by universal codes. Furthermore, we make it clear that the linkage of encoders enlarges the zero error rate region. It is interesting to note that the above results for the SWL system correspond in some sense to the previous results for the discrete memoryless channel with feedback.
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