Let $f : \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1\}$ be a 2-party function. For every product distribution $\mu$ on $\{0,1\}^n \times \{0,1\}^n$, we show that $${{CC}}^\mu_{0.49}(f) = O\left(\left(\log {{rprt}}_{1/4}(f) \cdot \log \log {{rprt}}_{1/4}(f)\right)^2\right),$$ where ${{CC}^\mu_\varepsilon(f)$ is the distributional communication complexity with error at most $\varepsilon$ under the distribution $\mu$ and ... more >>>

We study the problem of compressing interactive communication to its
information content $I$, defined as the amount of information that the
participants learn about each other's inputs. We focus on the case when
the participants' inputs are distributed independently and show how to
compress the communication to $O(I\log^{2}I)$ bits, with ... more >>>