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This paper investigates the classical modulo two sum problem in sourcecoding, but with a common observation: a transmitter observes $(X,Z)$, theother transmitter observes $(Y,Z)$, and the receiver wants to compute $X \oplusY$ without error. Through a coupling argument, this paper establishes a newlower bound on the sum-rate when $X-Z-Y$ forms a Markov chain.

Zero-Error Sum Modulo Two with a Common Observation