We prove a lower bound on the communication complexity of computing the $n$-fold xor of an arbitrary function $f$, in terms of the communication complexity and rank of $f$. We prove that $D(f^{\oplus n}) \geq n \cdot \Big(\frac{\Omega(D(f))}{\log \mathsf{rk}(f)} -\log \mathsf{rk}(f)\Big )$, where here $D(f), D(f^{\oplus n})$ represent the deterministic communication complexity, and $\mathsf{rk}(f)$ is the rank of $f$. Our methods involve a new way to use information theory to reason about deterministic communication complexity.

翻译：我们针对任意函数$f$的$n$重异或计算，基于$f$的通信复杂度与秩，证明了其通信复杂度的下界。我们证明了$D(f^{\oplus n}) \geq n \cdot \Big(\frac{\Omega(D(f))}{\log \mathsf{rk}(f)} -\log \mathsf{rk}(f)\Big )$，其中$D(f)$与$D(f^{\oplus n})$表示确定性通信复杂度，而$\mathsf{rk}(f)$为$f$的秩。我们的方法涉及一种利用信息论推理确定性通信复杂度的新途径。