Zero-Error Sum Modulo Two with a Common Observation

This paper investigates the classical modulo two sum problem in source coding, but with a common observation: a transmitter observes (X,Z), the other transmitter observes (Y,Z), and the receiver wants to compute X ⊕Y without error. Through a coupling argument, this paper establishes a new lower bound on the sum-rate when X −Z −Y forms a Markov chain.