  We provide the first capacity approaching coding schemes that robustly
simulate any interactive protocol over an adversarial channel that corrupts any
$\epsilon$ fraction of the transmitted symbols. Our coding schemes achieve a
communication rate of $1 - O(\sqrt{\epsilon \log \log 1/\epsilon})$ over any
adversarial channel. This can be improved to $1 - O(\sqrt{\epsilon})$ for
random, oblivious, and computationally bounded channels, or if parties have
shared randomness unknown to the channel.
  Surprisingly, these rates exceed the $1 - \Omega(\sqrt{H(\epsilon)}) = 1 -
\Omega(\sqrt{\epsilon \log 1/\epsilon})$ interactive channel capacity bound
which [Kol and Raz; STOC'13] recently proved for random errors. We conjecture
$1 - \Theta(\sqrt{\epsilon \log \log 1/\epsilon})$ and $1 -
\Theta(\sqrt{\epsilon})$ to be the optimal rates for their respective settings
and therefore to capture the interactive channel capacity for random and
adversarial errors.
  In addition to being very communication efficient, our randomized coding
schemes have multiple other advantages. They are computationally efficient,
extremely natural, and significantly simpler than prior (non-capacity
approaching) schemes. In particular, our protocols do not employ any coding but
allow the original protocol to be performed as-is, interspersed only by short
exchanges of hash values. When hash values do not match, the parties backtrack.
Our approach is, as we feel, by far the simplest and most natural explanation
for why and how robust interactive communication in a noisy environment is
possible.
