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 $X \oplus Y$ 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.

翻译：本文调查了源代码中古老的modulo两个和两个和的问题,但有一个共同点:一个发报机观察(X,Z)美元,另一个发报机观察(Y,Z)美元,接收器想无误地计算(Y,Z)美元。 本文通过合并论证,在X-Z-Y美元形成马可夫链时,对总和设定了新的下限。