Interactive Channel Capacity

In a profoundly influential 1948 paper, Claude Shannon defined the entropy function H, and showed that the capacity of a symmetric binary channel with noise rate (bit flip rate) eps is 1−H(eps). This means that one can reliably communicate n bits by sending roughly n/(1−H(eps)) bits over this channel. The extensive study of interactive communication protocols in the last decades gives rise to the related question of finding the capacity of a noisy channel when it is used interactively. We define interactive channel capacity as the minimal ratio between the communication required to compute a function (over a non-noisy channel), and the communication required to compute the same function over the eps-noisy channel. We show that the interactive channel capacity is roughly 1−Θ(H(eps)‾‾‾‾‾‾√). Our result gives the first separation between interactive and non-interactive channel capacity. Joint work with Ran Raz.