We define the $\textit{marginal information}$ of a communication protocol, and use it to prove XOR lemmas for communication complexity. We show that if every $C$-bit protocol has bounded advantage for computing a Boolean function $f$, then every $\tilde \Omega(C \sqrt{n})$-bit protocol has advantage $\exp(-\Omega(n))$ for computing the $n$-fold xor $f^{\oplus n}$. We prove exponentially small bounds in the average case setting, and near optimal bounds for product distributions and for bounded-round protocols.

翻译：我们定义了通信协议的$\textit{边际信息}$，并利用它证明了通信复杂性的异或引理。我们证明，如果每个$C$比特协议在计算布尔函数$f$时都具有有界优势，那么每个$\tilde \Omega(C \sqrt{n})$比特协议在计算$n$重异或$f^{\oplus n}$时，其优势为$\exp(-\Omega(n))$。我们在平均情形下证明了指数级小界，并在乘积分布和有界轮协议下给出了近乎最优的界。